1 Answer

Marco Pietro Cirillo · Answer 1 · 2021-08-09T08:19:41+0000

Answer:

54m²

Explanation:

You can use the Heron's formula:

A=√(p(p-a)(p-b)(p-c))

where

p - half of perimeter

a, b, c - lengths of sides

We have

$a=12m;\ b=15m;\ c=9m$

Calculate:

$p=(12+15+9)/(2)=(36)/(2)=18\ (m)\\\\A=√(18(18-12)+(18-15)(18-9))\\\\A=√((18)(6)(3)(9))\\\\A=√(2916)\\\\A=54\ (m^2)$

Let's check that it is not a right triangle.

If the sum of the squares of the two shorter sides is equal to the square of the longest side, then this triangle is rectangular.

We have

9m < 12m<15m

Check:

$9^2+12^2=81+144=225\\15^2=225$

This is a right trianglr wherew 9m and 12m are legs and 15m is a hypotenuse.

The formula of an area of a right triangle is:

A=(ab)/(2)

a, b - legs

Substitute:

$A=((9)(12))/(2)=(108)/(2)=54\ (m^2)$