Answer:
y = 54.1
Explanation:
The big triangle is divided in two: one on the left and one on the right. Lets start working with the right one.
We know the right triangle is a right triangle with legs 24 and 36, so we can use Pitagoras to find the hypotenuse (h), in a way that:
24^2 + 36^2 = h^2
1872 = h^2
Applying sqr root in both sides:
h = 43.27
So, the hypotenuse measures 43.27 or 43.3.
Now lets do the same with the triangle of the right which legs are 36 and y, lets find it hypotenuse (g):
36^2 + y^2 = g^2
1296 + y^2 = g^2
Now we will pass to the large triangle, which is composed by the left and the right triangles and has legs of 43.3 and g, and the hypotenuse is 24+y. Lets apply Pitagoras:
43.3^2 + g^2 = (24+y)^2
1875 + 1296 + y^2 = 24^2 + 48y + y^2
3171 + y^2 = 576 + 48y + y^2
As we have y^2 in both sides we can eliminate them
3171 + = 576 + 48y
Now subtract 576 in both sides:
3171 -576 = 576 + 48y - 576
2595 = 48y
Divide both sides by 48:
2595/48 = 48y/48
54.1 = y
So, the large hypotenuse measures 54.1+24 = 78.1. Lets verify:
43.3 ^2 + 1296 + 54.2^2 = 6,108.53
And the sqrd root of 6,108.53 is approximately 78.1. Verified!!!!
So, we can confirm: y = 54.1