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quadratics question

A garage door is 4m longer that it is wide and 1 m higher than it is wide.

The longest pole which can fit in side the garage is 7.5m long.

How wide is the garage?

Okay, I get the height to be x+1 , length to be x+4 and then the width to be x

This involves quadratics but surely the length equals x+4 as it fits in the garage? Meaning that x, the width is 3.5m?

But this is wrong according to the answers..
any ideas?

Reply 1

username667907

the longest distance will be a diagonal. try some 3d pythagoras.

Reply 2

madfish

Original post by Phredd

the longest distance will be a diagonal. try some 3d pythagoras.

so it would be (x+4)^2 + (x+1)^2 = 7.5?

Reply 3

davros

Original post by madfish

so it would be (x+4)^2 + (x+1)^2 = 7.5?

That's a diagonal across one side. Don't forget you are in 3 dimensions so you can have an even longer diagonal that involves the lengths of all 3 sides!

Reply 4

madfish

Original post by davros

That's a diagonal across one side. Don't forget you are in 3 dimensions so you can have an even longer diagonal that involves the lengths of all 3 sides!

ehhh I am not exactly sure what you mean :/

Reply 5

TenOfThem

Original post by madfish

ehhh I am not exactly sure what you mean :/

Have you done 3-D co-ordinates

Or any 3-D Pythagoras

For example , can you find the distance between (1, 2, 4) and (3, 6, 5)

Reply 6

madfish

Original post by TenOfThem

Have you done 3-D co-ordinates

Or any 3-D Pythagoras

For example , can you find the distance between (1, 2, 4) and (3, 6, 5)

nope I have never done that... wasnt on my GCSE course and I have not done it at alevel

Reply 7

Mr M

Study Forum Helper

Original post by madfish

nope I have never done that... wasnt on my GCSE course and I have not done it at alevel

Pythagoras in 2D:

c^2 = a^2 + b^2

Pythogaras in 3D:

d^2 = a^2 + b^2 + c^2

It certainly was part of your GCSE course.

Reply 8

TenOfThem

Original post by madfish

nope I have never done that... wasnt on my GCSE course and I have not done it at alevel

Ok

Well the diagonal in 3_D space is given by

d^2 = a^2 + b^2 + c^2

Reply 9

davros

Original post by madfish

nope I have never done that... wasnt on my GCSE course and I have not done it at alevel

Are you self-teaching or do you have a teacher who can go through this with you?

There's basically a very simple extension of Pythagoras's theorem from 2 dimensions to 3 dimensions that will help you solve this, but you probably need to do some practice questions with it to see what's going on.