There is a right angled triangle which has cathetes of 5,0 cm and 15 cm. You have to place a square inside this triangle so that two sides of the sqare will go along the two cathetes. And the tip of the square would touch the hypothenuse.
Question: How long is one side of the square ???
I know the answer, but I have no idea how to calculate this.
2007-11-23 23:51:31 · 3 answers · asked by in fact 1 in Science & Mathematics ➔ Mathematics
The equation of the hypotenuse is (axes the cathetes)
x/15+y/5=1
x+3y=15
If you take y= h and cut the hypotenuse you get x= 15-3h
so
h= 15-3h and h = 15/4 side of the square
In another way
using similitude
15/5=(15-h)/h so 15h =75-5h and h = 75/20= 15/4
2007-11-24 00:11:06 · answer #1 · answered by santmann2002 7 · 0⤊ 0⤋
From similar triangles
x/(15-x) = 5/15
so 15x = 75 - 5x
so 20x = 75
so x=3.75
This is the side of the square.
2007-11-24 00:01:45 · answer #2 · answered by Anonymous · 0⤊ 0⤋
cathetes?
easy question, but never seen the word cathetes
but you have 2 answers that agree
so I'll not bother further
2007-11-24 01:45:28 · answer #3 · answered by Anonymous · 0⤊ 0⤋