Question

A isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.​

Answer 1

$\bf\small{First,\:let\:the\:third\:side\:be\:x.}$

$\bf\tiny{It\:is\:given\:that\:the\:length\:of\:the \:equal\:sides\:us\:12cm\:and\:its\:perimeter\:is\:30 \:cm.}$

So,

30 = 12+12+x

⇒ 30 = 24 + x

⇒24 + x = 30

⇒ 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

$\bf\small{By\:using\:Heron's\:Formula,}$

$\bf \tiny\underline{Area\:of\:triangle:-}$= $\sqrt{s(s - a)(s - b)(s - c)}$

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

= $\sqrt{15 × 3 × 3 × 9}$

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