Question

How do you find the length of the roof of the house?

Answer 1

x = 50 ft

Explanation:

The question is Pythagoras theory

Pythagoras theory is given by the formula

Hypotenuse² = adjacent² + opposite²

from the question

Hypotenuse = x ft

adjacent = 40 ft

opposite = 30 ft.

Hypotenuse² = adjacent² + opposite²

= x² ft = 40² ft + 30² ft

= x² ft = 1600 ft + 900 ft

= x² ft = 2500 ft

`√(x2 \\ ) = √(2500) \\`

Note: the 2 square will cancel the square root.

living

`x = √(2500)`

x = 50 ft.

Note: tthe square root of 2500 is 50.

Answer 2

The length of the roof of the house, x, is 50 ft.

Explanation:

From observation of the given diagram, we can see that the length of the roof "x" is the hypotenuse of a right triangle. Therefore, we can use Pythagoras Theorem to calculate the value of x.

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

From observation of the given diagram, the lengths of the legs of the right triangle are 30 ft and 40ft, and the hypotenuse is x ft:

• a = 30 ft
• b = 40 ft
• c = x ft

Substitute the values of a, b and c into Pythagoras Theorem formula and solve for x:

`\implies 30^2+40^2=x^2`

`\implies 900+1600=x^2`

`\implies 2500=x^2`

`\implies x^2=2500`

`\implies {√(x^2)=√(2500)`

`\implies x=50`

Therefore, the length of the roof of the house is 50 ft.