Question

The perimeter of a triangle is 21 cm. Its two sides are 8.5 cm and 72 mm. Which of the following measurements gives the correct value of the third side?​

Answer 1

$\large\underline{ \underline{ \text{Question:}}}$

• The perimeter of a triangle is 21 cm. Its two sides are 8.5 cm and 72 mm. Which of the following measurements gives the correct value of the third side?

$\large\underline{ \underline{ \text{Solution:}}}$

Given that,

• $\text{The Perimeter of }\triangle \: \text{is} \: 21cm.$

And,

• $\text{The First side of }\triangle = 8.5 cm$
• $\text{The Second side of }\triangle = 72mm$

First we make the units same,

As we know,

$[1cm = 10mm]$

Hence,

$\text{The Perimeter of }\triangle = 21 \times 10mm$

• $\text{The Perimeter of }\triangle = 210mm$

And,

$\text{The First side of }\triangle = 8.5 \times 10mm$

• $\text{The First side of }\triangle = 85 mm$

As we know,

• $\boxed{\text{Perimeter}_{(\text{Triangle})} = a + b + c}$

Where a, b and c are the sides of triangle,

Let substitute the values,

$\implies 210mm = 85mm + 72mm + c$

Finding the value of c (The 3rd side of ∆),

$\implies 210mm = 157mm + c$

$\implies 210mm - 157mm = c$

$\implies { 53mm = c }$

Therefore,

• The Length of Third side of ∆ is 53mm.

$\\ \large\underline{ \underline{ \text{Required Answer:}}}$

• The Length of Third side of ∆ is 5.3cm.