Question

The perimeter of the rectangle below is 68 cm. The perimeter of the triangle is 60 cm. Find the length of the hypotenuse of the triangle​

Answer 1

The right triangle is assumed to be inscribed in the rectangle, such that

hypotenuse is the diagonal of the rectangle.

• The length of the hypotenuse of the triangle is 26 cm.

Reasons:

Let x and y represent the length of the sides of the rectangle

Whereby the base and height of the right triangle are the same as the

length and width of the rectangle, we have;

Perimeter of the rectangle = 2·x + 2·y = 68

Therefore;

$\displaystyle x + y = \frac{68}{2} = 34$

x + y = 34

The base of the right triangle = x

The height of the right triangle = y

By Pythagoras's theorem, the length of the hypotenuse side = √(x² + y²)

Therefore; Perimeter of the right triangle = x + y + √(x² + y²) = 60

Which gives;

∴√(x² + y²) = 60 - (x + y) = 60 - 34 = 26

The length of the hypotenuse side, √(x² + y²) = 26 cm

Learn more about Pythagoras's theorem here:

brainly.com/question/8171420