Question

the length of one leg of a right triangle is 15 m. The length of the other leg is 9 m shorter than the length of the hypotenuse. Find the length of the hypotenuse.

Answer 1

Let the hypotenuse is x

The length of the other leg is 9 m shorter than the length of the hypotenuse

The length of second leg = Hypotenuse - 9

The length of second leg = x - 9

the length of one leg of a right triangle is 15 m.

The first leg = 15m

Pythagoras Theorem : In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

Apply pythagoras for the value of x :

`\begin{gathered} \text{ Hypotenuse}^2=Base^2+Perpendicular^2 \\ x^2=15^2+(x-9)^2 \\ x^2=225+x^2+81-18x \\ x^2-x^2=225+81-18x \\ 18x=306 \\ x=(306)/(18) \\ x=17 \end{gathered}`

as x represent the hypotnuese, SO

Hypotenuse = 17m