Question

8. Calculate the Perimeter AND Area of

the RIGHT Triangle below.
17 m
10 m
21 m

Answer 1

`\text{Perimeter: }48\:\mathrm{m},\\\text{Area: }84\:\mathrm{m^2}`

Explanation:

The area of a triangle with side lengths
`a`,
`b`, and
`c` is given by:

`A=√(s(s-a)(s-b)(s-c))`, where
`s=(a+b+c)/(2)`

Substituting
`a=21, b=17, c=10`, we have:

`A=√(24(24-21)(24-17)(24-10)),\\A=√(24(3)(7)(14)),\\A=√(7,084),\\A=\boxed{84\:\mathrm{m^2}}`

The perimeter of a polygon is given by the sum of its sides. Since the triangle has sides 10, 17, and 21, its perimeter is
`10+17+21=\boxed{48\:\mathrm{m}}`.