Question

The base of an isosceles triangle is 4/5 cm .The perimeter of the triangle is 4 2/5cm .What is the length of eaither of the remaining equal sids?

Answer 1

Given :–

• Base of an Isosceles triangle = $\dfrac{4}{5}$cm.
• Perimeter of the triangle = $4\dfrac{2}{5}$cm.

To Find :–

• Length of either of the remaining equal sides.

Solution :–

Let,

∆ABC is an Isosceles triangle.

Base = BC = $\dfrac{4}{5}$cm

• AB = x

We know that,

Two sides of an Isosceles triangle is equal.

So,

• AC = x

Given that,

• Perimeter of an Isosceles = $4\dfrac{2}{5}$cm.

So, we need to convert mixed fraction into normal fraction.

So,

⟹ $\frac{4 \times 5 + 2}{5}$

⟹ $\frac{20 + 2}{5}$

⟹ $\frac{22}{5}$

Now, we need to find the value of other equal sides (x).

Perimeter = 2a + b

Where,

• a = x
• b = $\dfrac{4}{5}$
• Perimeter = $\dfrac{22}{5}$

⟹ $\dfrac{22}{5}$ = 2x + $\dfrac{4}{5}$

⟹ 2x + $\dfrac{4}{5}$ = $\dfrac{22}{5}$

⟹ 2x = $\dfrac{22}{5}$ – $\dfrac{4}{5}$

Now, take L.C.M. of the denominators (5 and 5) = 5.

⟹ 2x = $\dfrac{22 - 4}{5}$

⟹ 2x = $\dfrac{18}{5}$

⟹ x = $\dfrac{\cancel{18}}{5} \times \dfrac{1}{\cancel{2}}$

⟹ x = $\dfrac{9}{5}$

Now, convert fraction into mixed fraction.

For converting into mixed fraction, we need to divide the fraction $(\dfrac{9}{5})$.

★ refer to the 2nd attachment ★

So, the mixed fraction is $1\dfrac{4}{5}$

Hence,

The length of either of the remaining equal sides are $1\dfrac{4}{5}$cm