Question

The area of a right traingle is 270 square meters. The height of the right triangle is 15 meters. The length of the hypotenuse of the right triangle is __ meters

Answer 1

The length of the hypotenuse of the triangle is 39 meters.

Step by step explanation:

Area = 270 m^2

h = 15 m

Triangle area

`A\text{ = }(b\cdot h)/(2)`

Replace

`270\text{ = }\frac{b\cdot\text{ 15}}{2}`

Then we solve the equation.

`270\cdot2\text{ = b}\cdot15`
`540\text{ = b}\cdot15`
`b\text{ = }(540)/(15)\text{ = 36}`

Then we solve it by the Pythagorean theorem.

`a^2+b^2=c^2`

a = 15

b = 36

c = x

`15^2+36^2=x^2`
`x\text{ = }\sqrt[]{15^2+36^2}\text{ = }\sqrt[]{1521}`
`X\text{ = 39}`