Question

In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=3 feet and b=5 feet, what is the perimeter? If necessary, round to the nearest tenth.

Answer 1

The perimeter of the triangle 12 cm.

Explanation:

Given that,

In a right angled triangle, a and b are the length of the legs and c is length of the hypotenuse.

Pythagorean Theorem:

Sum of square of the legs is equal to square of hypotenuse.

∴
`a^2+b^2=c^2`

`a= ?`,
`a= 3` cm and
`b=5` cm

`a^2+3^2=5^2`

⇒
`a^2+9=25`

⇒
`a^2=25-9`

⇒
`a^2=16`

⇒
`a = 4`
`cm`

The perimeter of the triangle = sum of all sides

`=a+b+c`

`=(4+3+5)`
`cm`

`=12`
`cm`