Question

An isosceles triangle has perimeter 28 cm and each of the equal sides is 8 cm. Find the area of the triangle. with proper steps plzz!

Answer 1

Answer:

let the triangle be ABC

let sides of the triangle be ab,bc,ac

perimeter=28cm

AB=8cm , BC=8cm , AC=?

perimeter=28cm

AB+BC+AC=28

8+8+AC=28

AC=28-16=12

.°. AC=12cm

by heron's formula

$s = \frac{a + b + c}{2} = \frac{8 + 8 + 12}{2}$

$= \frac{28}{2} = 14$

$area = \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{14(14 - 8)(14 - 8)(14 - 12)}$

$= \sqrt{14 \times 6 \times 6 \times 2}$

$= 6 \sqrt{28}$

$= 6 \times 2 \sqrt{7}$

$12 \sqrt{7}$

.°.

$ar(abc) = 12 \sqrt{7} {cm}^{2}$

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