Question

The perimeter of an isosceles triangle is 42cm. It's base is 2/3 times the sum of equal side of the triangle.Find the length of each side.

Answer 1

Answer:

12.6 cm, 12.6 cm, 16.8 cm...

Step-by-step explanation:

$\text{Let each of the equal side be a. Then, sum of equal sides = a + a = 2a}\\\\\text{If the base is b, then,}\\\\b = \dfrac{2}{3} \times 2a = \dfrac{4}{3}a\\\\\text{Now, perimeter = a + a + b}\\\\= a + a + \dfrac{4}{3}a\\\\= \dfrac{3a+3a+4a}{3}\\\\= \dfrac{10}{3}a\\\\\text{But, given perimeter = 42 cm}\\\\\therefore \: \dfrac{10}{3}a = 42\\\\\implies a = 42 \times 3 \times \dfrac{1}{10}\\\\= 126 \div 10\\\\= \boxed{\boxed{\bold{12.6}}}\\\\\text{Thus, equal sides are 12.6 cm each.}$

$\text{And the unequal side is } \dfrac{4}{3} \times \dfrac{126}{10} = \text{16.8 cm}$