### The base of an isosceles triangle is 24 cm and the perimeter is 50 cm. Find the area of the triangle, if the base is not equal to the other two sides.

$60 \space cm^2$

Step by Step Explanation:
1. We are given an isosceles triangle, so two sides are equal.
Let's assume a = b.
the base (side c) = 24 cm.
Also, perimeter = 2S = 50
S =
 50 2
= 25
2. Now, Perimeter = a + b + c
or, 50 = 2a + c = 2a + 24
or, a =
 50 - 24 2
= 13
3. As per Heron's formula, the area of a triangle with sides a, b and c, and perimeter 2S = $\sqrt{ S(S-a)(S-b)(S-c) }$
4. As a = b.
∴ Area $= \sqrt{ S(S-a)(S-a)(S-c) }$$= (S-a)\sqrt{ S(S-c) }$
5. On substituting a = 13 , c= 24 and S = 25, we get:
Area $= (25 - 13)\sqrt{ 25(25 - 24) }$$= 12 \sqrt { 25 \times 1}$$= 60 \space cm^2$