Question

The base of an isosceles triangle is 5/2 cm. The perimeter of the triangle is 4 1/10 cm. What is the length of either of the remaining equal sides?

Answer 1

Answer:

$\sf \dfrac{4}{5}$ cm

$\Large {\underline { \sf {Clarification :}}}$

Here, we are provided that the base of an isosceles triangle is $\sf \dfrac{5}{2}$ cm. And, the perimeter of the triangle is $\sf 4 \dfrac{1}{10}$ cm. We are asked to calculate the length of either of the remaining sides.

Basic concept and steps :

• Isosceles triangle is a triangle with any two sides equal.

So,

• Step 1 : We'll assume the remaining sides as "x cm" each. (As length of both sides are same.) [Assumption]

• Step 2 : We know the formula of the perimeter of the triangle that, is sum of all sides. This formula will act as a linear equation here. We will formulate a linear equation. [Forming an equation.]

• Step 3 : After forming an equation, we'll solve for x that is our required answer. [Solving the equation to find the value of x.]

$\Large {\underline { \sf {Explication \; of \; steps :}}}$

As per the provided information in the given question, we have :

• Base of the isosceles triangle = $\sf \dfrac{5}{2}$ cm

• Perimeter of the ∆ = $\sf 4 \dfrac{1}{10}$ cm ⇒ $\sf \dfrac{41}{10}$ cm

We are asked to find the length of either of the remaining equal sides.

Let us assume the length of the remaining sides as x cm each.

We know that,

★ Perimeter of ∆ = Sum of all sides

⇒ $\sf \dfrac{41}{10}$ cm = $\sf \dfrac{5}{2}$ cm + x cm + x cm

⇒ $\sf \dfrac{41}{10}$ cm = $\sf \dfrac{5}{2}$ cm + 2x cm

⇒ $\sf \dfrac{41}{10}$ cm = $\sf \dfrac{5+4x}{2}$ cm

⇒ $\sf \dfrac{41}{10}$ × 2 cm = 5 + 4x cm

⇒ $\sf \dfrac{41}{5}$ cm = 5 + 4x cm

⇒ $\sf \dfrac{41}{5}$ cm - 5 = 4x cm

⇒ $\sf \dfrac{41 - 25}{5}$ cm = 4x cm

⇒ $\sf \dfrac{16}{5}$ cm = 4x cm

⇒ $\sf \dfrac{16}{5}$ cm ÷ 4 = x cm

⇒ $\sf \dfrac{16}{5} \times \dfrac{1}{4}$ cm = x cm

⇒ $\sf \dfrac{4}{5} \times \dfrac{1}{1}$ cm = x cm

$\longrightarrow \underline{\boxed{\sf{ \dfrac{4}{5} \; cm = x \; cm}}} \; \bigstar$

$\therefore$ The length of either of the remaining equal sides is $\sf \dfrac{4}{5}$ cm.