Question

As isoscels triangle has perimeter 30 cm and each of the equal sides is 12cm find area of the triangle

Answer 1

Answer:

Step-by-step explanation: let ABC be the triangle and AB =AC.

AB=12 cm

AC=12 cm

BC=30-(12+12)

=6 cm

By pathagoras theorum

Semi perimeter =30/2=15 cm

Area of triangle =√15(15-12)(15-12)(15-6)

=√15×3×3×9

=9√15 cm^2 solved

Answer 2

First,let the third side be x.

It is given that the length of the equal sides us 12 cm and it's perimeter is 30 cm.

So,$30=12+12+x$

$⇒ 30 = 24 + x$

$⇒24 + x = 30$

$⇒ x= 30 - 24$

$⇒ x = 6$

So,the length of the third side is 6 cm.

Thus,the semi perimeter of the isosceles triangle (s) = 30/2 cm =15 cm

By using Heron's Formula,

Area of the triangle,

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

$= \sqrt{15(15 - 12)(15 - 12)(15 - 6)} \: {cm}^{2}$

$= \sqrt{15 \times 3 \times 3 \times 9} \: {cm}^{2}$

$= 9 \sqrt{15} \: {cm}^{2}$