Question

the equal sides of the isosceles triangle are 12 cm and the perimeter is 30 cm. the area of this triangle is?
(a) 9√15cm sqare
(b) 6√15cm sqare
(c) 3√15cm sqare
(d) √15cm sqare ​

Answer 1

Given info : The equal sides of the isosceles triangle are 12 cm and the perimeter is 30 cm.

To find : The area of this triangle is ...

Solution : let a , a and b are sides of isosceles triangle.

so, perimeter , 2S = a + a + b = 2a + b = 30......(1)

Here a = 12

So, b = 30 - 2 × 12 = 30 - 24 = 6

Now, area of triangle using Heron's formula, A = √{s(s - a)(s - b)(s - c)}

Here semi perimeter, s = 30/2 = 15

= √{15(15 - 12)(15 - 12)(15 - 6)}

= √{15 × 3 × 3 × 9}

= 9√15 cm²

Therefore the area of isosceles triangle is 9√15 cm². I.e., option (a) is correct choice