Question

Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a to the power of 5 and 9a to the power of 5.

Answer 1

`36a^5`.

Explanation:

In a right angle triangle,

Length of one leg
`=12a^5`

Length of other leg
`=9a^5`

According to the Pythagoras theorem,

`Hypotenuse^2=leg_1^2+leg_2^2`

Using Pythagoras theorem,

`Hypotenuse^2=(12a^5)^2+(9a^5)^2`

`Hypotenuse^2=144(a^5)^2+81(a^5)^2`

`Hypotenuse=√(225(a^5)^2)`

`Hypotenuse=15a^5`

Perimeter of right angle triangle is the sum of all sides of the triangle.

`Perimeter=12a^5+9a^5+15a^5`

`Perimeter=36a^5` units.

Therefore, the required expression is
`36a^5`.