Question

ANSWER ASAP!! Find the area of a triangle with legs that are: 12 m, 15 m, and 9 m.

Answer 1

Answer:

54m²

Step-by-step explanation:

METHOD 1:

You can use the Heron's formula:

$A=\sqrt{p(p-a)(p-b)(p-c)}$

where

p - half of perimeter

a, b, c - lengths of sides

We have

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

Calculate:

$p=\dfrac{12+15+9}{2}=\dfrac{36}{2}=18\ (m)\\\\A=\sqrt{18(18-12)+(18-15)(18-9)}\\\\A=\sqrt{(18)(6)(3)(9)}\\\\A=\sqrt{2916}\\\\A=54\ (m^2)$

METHOD 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:

$A=\dfrac{ab}{2}$

a, b - legs

Substitute:

$A=\dfrac{(9)(12)}{2}=\dfrac{108}{2}=54\ (m^2)$