Question

Find the area of the isosceles triangle, if the perimeter is 13 cm and the base is 5 cm

Answer 1

$\bf \LARGE \it Hey \: User!!!$

given :-

• base of the isosceles triangle = 5cm
• perimeter of the isosceles triangle = 13cm

we know that 2 sides of an isosceles triangle are equal.

here base is given, hence other two sides of the isosceles triangle must be equal.

let the equal sides of the isosceles triangle be x and y.

y = x

therefore 5 + x + y = 13cm
>> 5 + x + x = 13cm
>> 2x = 13 - 5
>> 2x = 8
>> x = 8/2
>> x = 4cm

the other two equal sides of the isosceles triangle is 4cm each.

now, we have to find it's area.

we can find it's area by two methods.

let the sides of the isosceles triangle be a, b and c.

semi-perimeter of the triangle = 13/2 = 7.5cm

$\rm \small area \: of \: the \: triangle \: by \: herons \: \rm formula \\ \rm \small= \sqrt{s(s - a)(s - b)(s - c)} \: \\ \rm \small = \sqrt{7.5(7.5 - 5)(7.5 - 4)(7.5 - 4)} \\ \rm \small = \sqrt{7.5 \times 2.5 \times 3.5 \times 3.5} \\ \rm \small = \sqrt{229.6875} \\ \rm \small = {15.15cm}^{2}$

$\bf \LARGE \it Cheers!!!$