Question

Please Help!! much appreciated! :D Find the value of y.

Answer 1

In the largest triangle, the missing side has length

√((11 + 5)² - x ²) = √(256 - x ²)

But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as

√(11² + y ²) = √(121 + y ²)

so that

√(256 - x ²) = √(121 + y ²)

or, by taking the squares of both sides,

256 - x ² = 121 + y ²

y ² = 135 - x ²

In the smallest triangle, you have

5² + y ² = x ²   ==>   x ² = 25 + y ²

Substitute this into the previous equation and solve for y :

y ² = 135 - (25 + y ²)

y ² = 110 - y ²

2y ² = 110

y ² = 55

y = √55