Question

A rectangle is 5 cm long and 3 cm wide. Its perimeter is doubled when each of its sides is increased by x cm. Find an equation in x and find its new length ​

Answer 1

Given :-

• Length of rectangle = 5cm
• Width of rectangle = 3cm

To Find :-

• The new length of rectangle = ?

Solution :-

We will solve this question by applying formula of of rectangle . As given in the question that a rectangle is 5 cm long and 3 cm wide. Its perimeter is doubled when each of its sides is increased by x cm.

Calculation begin :-

⟹ New length = 5 + x

⟹ New width = 3 + x

Formula Used :-

⟹ Perimeter of rectangle = 2(length + wide)

⟹ 2(length + wide) = double of its perimeter

⟹ 2(5 + x + 3 + x) = 2(5 + 3) × 2

⟹ 2(8 + 2x) = 4(5 + 3)

⟹ 16 + 4x = 4 × 8

⟹ 16 + 4x = 32

⟹ 4x = 32 - 16

⟹ 4x = 16

⟹ x = 4cm

⟹ So, New length = 5 + x => 5 + 4 = 9cm

⟹ So, New width = 3 + x => 3 + 4 = 7cm

Hence,

• The new length of rectangle = 5 + x
• The new length of rectangle = 5 + 4
• The new length of rectangle = 9cm

Answer 2

Answer:

Given :-

• A rectangle is 5 cm long and 3 m wide(breadth).
• Its perimeter is doubled when each of its sides is increased by x cm.

To Find :-

• What is the new length of rectangle.

Formula Used :-

$\clubsuit$ Perimeter of a Rectangle Formula :

$\longmapsto \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}$

Solution :-

First, we have to find the original perimeter of rectangle :

$\implies \sf Original\: Perimeter_{(Rectangle)} =\: 2(5 + 3)$

$\implies \sf Original\: Perimeter_{(Rectangle)} =\: 10 + 6$

$\implies \sf \bold{\green{Original\: Perimeter_{(Rectangle)} =\: 16\: cm}}$

Let,

$\mapsto$ New length = (5 + x) cm

$\mapsto$ New breadth = (3 + x) cm

According to the question by using the formula we get,

$\implies \sf 2\{(5 + x) + (3 + x)\} =\: 2 \times 16$

$\implies \sf 2(5 + x + 3 + x) =\: 32$

$\implies \sf 10 + 2x + 6 + 2x =\: 32$

$\implies \sf 10 + 6 + 2x + 2x =\: 32$

$\implies \sf 16 + 4x =\: 32$

$\implies \sf 4x =\: 32 - 16$

$\implies \sf 4x =\: 16$

$\implies \sf x =\: \dfrac{\cancel{16}}{\cancel{4}}$

$\implies \sf x =\: \dfrac{4}{1}$

$\implies \sf\bold{\purple{x =\: 4\: cm}}$

Hence, the required new length and breadth are :

$\mapsto$ New length of Rectangle :

$\longrightarrow \sf (5 + x)\: cm$

$\longrightarrow \sf (5 + 4)\: cm$

$\longrightarrow \sf\bold{\red{9\: cm}}$

$\mapsto$ New breadth of Rectangle :

$\longrightarrow \sf (3 + x)\: cm$

$\longrightarrow \sf (3 + 4)\: cm$

$\longrightarrow \sf\bold{\red{7\: cm}}$

$\therefore$ The new length of rectangle is 9 cm .