### The perimeter of an isosceles triangle is 64 cm. The ratio of the equal side to its base is 5 : 6. Find the area of the triangle.

**Answer:**

192 cm^{2}

**Step by Step Explanation:**

- Let's assume, the lengths of the base and the equal sides of the isosceles triangle are
**b**cm and**x**cm respectively.

Following figure shows the isosceles triangle ABC,

The ratio of the equal side to its base is 5 : 6.

Therefore,

=5 6 **x****b**

By cross multiplying, we get:**b**=

------(1)6 **x**5 - According to the question, the perimeter of the isosceles triangle ABC = 64 cm

Therefore,**x**+**x**+**b**= 64

⇒ 2**x**+

= 646 **x**5 **[From equation (1),****b**=

]6 **x**5

⇒

= 6410 **x**+ 6**x**5

⇒ 10**x**+ 6**x**= 320

⇒ 16**x**= 320

⇒**x**= 20 cm - Putting the value of
**x**in equation (1), we get:**b**=

= 24 cm120 5 - The area of the isosceles triangle ABC can be calculated using Heron's formula, since all sides of the triangle are known.

S =

= 32 cm64 2

The area of the isosceles triangle ABC = √S(S - AB)(S - BC)(S - CA)

= √32(32 - 24)(32 - 20)(32 - 20)

= 192 cm^{2} - Thus, the area of the triangle is 192 cm
^{2}.