You are Here: Home >< A-levels

# Maths Question Help

Announcements Posted on
TSR's new app is coming! Sign up here to try it first >> 17-10-2016
1. Hi, could someone explain to me why my approach to the following question doesn't work? Three squares are arranged as shown so that their baseslie on a straight line. Also, the corners P, Q and R lieon a straight line. The middle square has sides that are8 cm longer than the sides of the smallest square. Thelargest square has sides of length 50 cm. There are twopossible values for the length (in cm) of the sides of thesmallest square.

https://www.ukmt.org.uk/pdfs/SMC2015_sol_extended.pdf

question 19 in the solutions, there is a diagram.

I started by calculating the gradient of the first point to the second point...

which is 8/x

I then calculated the gradient from the first point to the last point...

which is (50-x)/(x+8)

I then equated the two gradients...

8/x = (50-x)/(x+8)

8 = x(50-x)/(x+8)

8x + 64 = 50x - x^2

x^2 - 42x + 64 = 0

However this quadratic is not soluble without a calculated (at least by me)

Thanks for any help
2. (Original post by staircase)

I then calculated the gradient from the first point to the last point...

which is (50-x)/(x+8)
It doesn't work because of that.

The vertical change is indeed 50-x between the largest and smallest squares, however the horizontal change is x+(x+8) because (x+8) on its own only accounts for the length of the middle square whereas you need the smaller square as well, which is the x.

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: October 16, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How does exam reform affect you?

From GCSE to A level, it's all changing

Poll

## All the essentials

### Student life: what to expect

What it's really like going to uni

### Essay expert

Learn to write like a pro with our ultimate essay guide.

### Create a study plan

Get your head around what you need to do and when with the study planner tool.

### Resources by subject

Everything from mind maps to class notes.

### Study tips from A* students

Students who got top grades in their A-levels share their secrets