The area of the isosceles triangle is 5/4√11 cm^2, if the perimeter is 11 cm and the base is 5 cm.

Question

Write True or False and justify your answer:

The area of the isosceles triangle is 5/4√11 cm², if the perimeter is 11 cm and the base is 5 cm.

Answer 1

True

Justification:

According to the question,

Perimeter = 11 cm

And base, a = 5

As the triangle is isosceles, b = c

Perimeter = 11

⇒ a + b + c = 11

⇒ 5 + b + b = 11

⇒ 5 + 2b = 11

⇒ 2b = 6

⇒ b = 3

So, we have,

a = 5, b = 3, c = 3

s = (a + b + c)/2

⇒ s = (5 + 3 + 3)/2 = 11/2

Area of triangle = √s(s-a)(s-b)(s-c)

⇒ Area of triangle = (5√11)/4 cm²

Hence, the statement “The area of the isosceles triangle is 5/4√11 cm², if the perimeter is 11 cm and the base is 5 cm” is True.