Question

the roof of a house is the shape of an isosceles right triangle as shown in the diagram below. what is the height of the roof, h? 10 ft h 5 ft 5√2 ft 5√3 ft (5√2)/2 ft

Explanation:

Step1: Find base of small right triangle

First, identify the large isosceles right triangle with legs = 10 ft. The height \( h \) splits it into two congruent isosceles right triangles, so the base of each small triangle is \( \frac{10}{\sqrt{2}} = 5\sqrt{2} \) ft.

Step2: Use Pythagoras for height \( h \)

For the small right triangle: hypotenuse = 10 ft, one leg = \( 5\sqrt{2} \) ft. Solve for \( h \):
$$h = \sqrt{10^2 - (5\sqrt{2})^2}$$
$$h = \sqrt{100 - 50} = \sqrt{50} = 5\sqrt{2}$$

Answer:

B. \( 5\sqrt{2} \) ft