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# 3.The base of an isosceles triangle is $$\frac{4}3$$ cm. The perimeter of the triangle is $$4\frac{2}{15}$$ cm. What is the length of either of the remaining equal sides?

We have length of base as $$\frac{4}3$$
Let the length of the equal sides by each of x.

Perimeter of the isosceles triangle=sum of the base +sum of two equal sides=$$4\frac{2}{15}$$

$$\qquad = (\frac{4}3+x+x)cm =4\frac{2}{15}$$

∴ $$2x+\frac{4}3=4\frac{2}{15}$$

$$\Rightarrow 2x+\frac{4}3=\frac{62}{15}$$

$$\Rightarrow 2x=\frac{62}{15}-\frac{4}3\quad$$[Transposing $$\frac{4}3$$ from (+) to (-)]

$$\Rightarrow 2x=\frac{62-20}{15}$$

$$\Rightarrow 2x=\frac{42}{15}$$

$$\Rightarrow x=\frac{42}{15}÷2\quad$$[Transposing 2 from (x) to ÷]

$$\Rightarrow x=\frac{42}{15}×\frac{1}2$$

$$\Rightarrow x=\frac{7}{5}=1\frac{2}5$$

Hence, the length of each equal side is =$$1\frac{2}5$$