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

Answer:

$36a^5$.

Step-by-step 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,

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

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

$Hypotenuse=\sqrt{225(a^5)^2}$

$Hypotenuse=15a^5$

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 $36a^5$.