Question

if the perimeter of an isosceles triangle is 11 cm and its an equal side is 5 cm find its area

Answer 1

Dear student
assuming " its an equal side"="its unequal side"
An isosceles triangle has 2 equal sides and one inequal side

So,
Let the equal side be "x"
so the sides of isosceles triangle are

a = x
b = x
c = 5

Perimeter = a + b + c

=> 11 = x + x + 5

=> 11 - 5 = 2x

=> 6 = 2x

=> 6/2 = x

=> 3 = x

Therefore,
Sides are 3, 3, 5

s = Perimeter/2

s = 11/2

s = 5.5



$$\begin{gathered} Area=\sqrt{s(s-a)(s-b)(s-c)} \\ Area=\sqrt{5.5\times (5.5-3)(5.5-3)(5.5-5)} \\ Area=\sqrt{5.5\times 2.5\times 2.5\times 0.5} \\ Area=\sqrt{(11\times 0.5)\times (5\times 0.5)\times (5\times 0.5)\times 0.5} \\ Area=0.5\times 5\times 0.5\sqrt{11} \\ Area=1.25\sqrt{11}c{m}^2 \\ Area=4.1457809879.. \\ or \\ Area=4.14c{m}^2 \\ regards \end{gathered}$$