GCSE Maths (Higher) - Mock Exam Question

Hi Everyone,

Adult learner here hoping someone can help me with a question I am stuck on.

Question:
The lengths of the sides of two squares are integers, when measured in cm. The difference between the areas of the two squares is 36cm^2

Find the lengths of the sides of the two squares.

I would appreciate any help or pointers.

-Ben

Reply 1

Moltenmo

15

Original post by BenAnnaMan

Hi Everyone,

Adult learner here hoping someone can help me with a question I am stuck on.

Question:
The lengths of the sides of two squares are integers, when measured in cm. The difference between the areas of the two squares is 36cm^2

Find the lengths of the sides of the two squares.

I would appreciate any help or pointers.

-Ben

I might be giving too much away here but you need to find two square numbers that subtract to give 36cm. Then the rest should be easy.

Posted from TSR Mobile

Reply 2

BenAnnaMan

OP

7

Original post by Moltenmo

I might be giving too much away here but you need to find two square numbers that subtract to give 36cm. Then the rest should be easy.

Posted from TSR Mobile

Hi Moltenmo,

Thanks for the reply.

By writing out 1^2 through to 12^2 i can see that the difference between 10^2 and 8^2 is 36, therefor giving me the answer of 8cm and 10cm.

Say for example the question was modified slightly to say "The lengths of the sides of two squares are integers, when measured in cm. The difference between the areas of the two squares is 561cm^2. Find the lengths of the sides of the two squares." I would not have enough time to write all the square numbers down and try and work out the difference. Is there a formula i should be following?

I have attampted the following, but it is wrong.

x^2 - y^2 = 36 (the equation from the question)
x^2 = y^2 + 36 (rearange to split x and y)
x = y + 6 (square root to give me the length of the sides)

(y + 6)^2 = y^2 +36 (plug the value of the x side from above into the area formula)
y^2 + 12y + 36 = y^2 + 36 (expand brackets)
12y = 0 (Cancel/simplify)

I feel like I am missing something with this question or am I over thinking it?

-Ben

Reply 3

Moltenmo

15

Original post by BenAnnaMan

Hi Moltenmo,

Thanks for the reply.

By writing out 1^2 through to 12^2 i can see that the difference between 10^2 and 8^2 is 36, therefor giving me the answer of 8cm and 10cm.

Say for example the question was modified slightly to say "The lengths of the sides of two squares are integers, when measured in cm. The difference between the areas of the two squares is 561cm^2. Find the lengths of the sides of the two squares." I would not have enough time to write all the square numbers down and try and work out the difference. Is there a formula i should be following?

I have attampted the following, but it is wrong.

x^2 - y^2 = 36 (the equation from the question)
x^2 = y^2 + 36 (rearange to split x and y)
x = y + 6 (square root to give me the length of the sides)

(y + 6)^2 = y^2 +36 (plug the value of the x side from above into the area formula)
y^2 + 12y + 36 = y^2 + 36 (expand brackets)
12y = 0 (Cancel/simplify)

I feel like I am missing something with this question or am I over thinking it?

-Ben

As this is a GCSE question, I think I am right in assuming that you're only expected to be able to list square numbers and figure out which pair subtracts to give the answer. I also don't remember learning any formula. Unfortunately, it's a bit of guess work. :smile:

Posted from TSR Mobile

(edited 6 years ago)

Reply 4

Moltenmo

15

_-

(edited 6 years ago)

Reply 5

username2740239

12

Yeah i think you only need to write out 1 4 9 16 25 36 49 64 81 100 (square numbers) and notice that 64 + 36 is 100, so it's 8 and 10

Reply 6

BenAnnaMan

OP

7

Thanks for the replys :smile:

Looks like I am overthinking this. This type of question has just become orders of magnitude easier than I originally thought.

-Ben

Reply 7

Brumafriend

11

Original post by BenAnnaMan

Hi Moltenmo,

Thanks for the reply.

By writing out 1^2 through to 12^2 i can see that the difference between 10^2 and 8^2 is 36, therefor giving me the answer of 8cm and 10cm.

Say for example the question was modified slightly to say "The lengths of the sides of two squares are integers, when measured in cm. The difference between the areas of the two squares is 561cm^2. Find the lengths of the sides of the two squares." I would not have enough time to write all the square numbers down and try and work out the difference. Is there a formula i should be following?

I have attampted the following, but it is wrong.

x^2 - y^2 = 36 (the equation from the question)
x^2 = y^2 + 36 (rearange to split x and y)
x = y + 6 (square root to give me the length of the sides)

(y + 6)^2 = y^2 +36 (plug the value of the x side from above into the area formula)
y^2 + 12y + 36 = y^2 + 36 (expand brackets)
12y = 0 (Cancel/simplify)

I feel like I am missing something with this question or am I over thinking it?

-Ben

Hey. What I believe you're doing wrong is fairly simple.

x^2 = y^2 + 36 (rearange to split x and y)

x = y + 6 (square root to give me the length of the sides)

I think this is where you went wrong. Square rooting a number like x^2 means you are dividing it by x, square rooting y^2 means you're dividing it by y, and square rooting 36 means you're dividing it by 6.

This means you're dividing each entity, I guess, in the equation by a different amount.

For example: "4+4=8"
However: "2+2≠2.83" (3 s.f)

I believe that this is where you went wrong. :smile:

Reply 8

TheMightyBadger

13

Original post by BenAnnaMan

Hi Moltenmo,

Thanks for the reply.

By writing out 1^2 through to 12^2 i can see that the difference between 10^2 and 8^2 is 36, therefor giving me the answer of 8cm and 10cm.

Say for example the question was modified slightly to say "The lengths of the sides of two squares are integers, when measured in cm. The difference between the areas of the two squares is 561cm^2. Find the lengths of the sides of the two squares." I would not have enough time to write all the square numbers down and try and work out the difference. Is there a formula i should be following?

I have attampted the following, but it is wrong.

x^2 - y^2 = 36 (the equation from the question)
x^2 = y^2 + 36 (rearange to split x and y)
x = y + 6 (square root to give me the length of the sides)

(y + 6)^2 = y^2 +36 (plug the value of the x side from above into the area formula)
y^2 + 12y + 36 = y^2 + 36 (expand brackets)
12y = 0 (Cancel/simplify)

I feel like I am missing something with this question or am I over thinking it?

-Ben

x ≠ y + 6. When you have:

x^2 = y^2 + 36, it means that:

x = sqrt(y^2 + 36) because you have to square root the whole of both sides of the equation, not each individual component.