unknown measurements of a staircase

Question

question:"roiled has 4.8m of oregon timber he wishes to use to make steps. he needs 5 steps to rise a total height of 1.2 metres from the ground. he uses all the wood to construct the steps, including supports. find x (the flat part of each step) and y (look at diagram below if that helps, sorry the pic is flipped but i couldn't turn it around)"

I have figured out that the height of each step is 240cm therefore he has 4460m of timbre left. Take a further 1200cm away from that for one of the supports leaves him with 3260m of timbre. so far that is all I figured out as i can't find the formula for finding x and y. I know that y= a squared+b squared but there is no b or a. any help would be appreciated.

i figured out i just need to know how to find x which is the base so i know that the height is 24cm how do i find the base of the triangle

sorry about the tag i wasn't sure which one to put so i sort of chose anything.

Answer 1

The base should be equal to the sum of x, that is 5x (as we can see that the x sides are parallel to the base). And we know that the hypotenuse is the sum of y, that is 5y

So using Pythagoras theorem, (5y)^2 = (5x)^2 + 1.2^2

That's what I've figured out so far.

Answer 2

Sorry you don't need that equation I posted before.

So as I said before the sum of the x are equal to the base since they are parallel

So we have a total of 5x+5x=10x. You know that the height of each stair is 0.24m and the height of the whole thing is 1.2 m

Therefore 10x+ 5(0.24) + 1.2 =4.8

      10x = 2.4
      X   = 2.4/10
          = .24

Therefore base = 5x = 1.2 m