Question

the perimeter of an isosceles triangle is 30 cm and two of its equal sides measure 12 cm. Find the area of triangle

Answer 1

$Given\\ \\ Perimeter\:\:of\:\:triangle = sum\:\:of\:\:all\:\:sides\\Base + two\:other\:sides\:\:i.e\:slanting\:sides = 30 cm\\Base + 12 +12 = 30 \\Base = 30-24=8\:cm$

Answer 2

First,let the third side be x.

It is given that the length of the equal sides is 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,

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

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

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

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