Find the area of a triangle whose two sides are 12 inches and 14 inches long, and has a perimeter of 34 inches.

Question

asked Apr 5, 2021 205k views

1 Answer

Patronaut · Answer 1 · 2021-04-09T04:54:59+0000

Answer:

$\huge\boxed{A=3√(255)\ in^2\approx47.91\ in^2}$

Explanation:

We have two sides

$a=12in;\ b=14in$

and the preimeter

P=34in

We can calculate the length of the third side:

c=P-a-b

substitute

$c=34-12-14=8\ (in)$

Use the Heron's formula:

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

where

p=(P)/(2)

substitute:

$p=(34)/(2)=17\ (in)\\\\A=√(17(17-12)(17-14)(17-8))=√((17)(5)(3)(9))\\\\=√(9)\cdot√((17)(5)(3))=3√(255)\ (in^2)\approx47.91\ (in^2)$