Question

The length of a rectangle is 4 cm more than its breadth. The perimeter of the rectangle is 40 cm. Find the length and breadth of the rectangle ?

Answer 1

$\huge\purple{ \underline{ \boxed{\mathbb\colorbox{cyan}{\red{QUESTION : }}}}}$

The length of a rectangle is 4 cm more than its breadth. The perimeter of the rectangle is 40 cm. Find the length and breadth of the rectangle ?

$\huge\purple{ \underline{ \boxed{\mathbb\colorbox{cyan}{\red{ANSWER : }}}}}$

Length of rectangle = 12 cm

Breadth of rectangle = 8 cm

$\huge\purple{ \underline{ \boxed{\mathbb\colorbox{cyan}{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

The length of a rectangle is 4 cm more than its breadth.

The perimeter of the rectangle is 40 cm.

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

The length and breadth of the rectangle .

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED: }}}}$

$\purple{ \boxed{ \textsf{Perimeter of rectangle = 2 \: ( L + B)}}}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

Let breadth of rectangle = x cm

Then length of rectangle = x + 4 cm

$\red{ \underline{\underline{ \textbf{According to question : }}}}$

$\textsf{Perimeter of rectangle = 2 \: ( L + B)}$

$\displaystyle \longrightarrow \bf40 \: cm = 2 \: (x + 4 + x) \\ \\ \displaystyle \longrightarrow \bf40 \: cm = 2 \: (2x + 4) \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf40 \:cm = 4x + 8 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf4x + 8 = 40 \: cm \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf4x = 40 - 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf4x = 32 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf x = \frac{32}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf x = 8 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \begin{array}{l} \textsf{Breadth of rectangle = x = 8 cm}\\ \\ \textsf{Length of rectangle = x + 4 = 8 + 4 = 12 \: cm }\end{array}}}$

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb\colorbox{cyan}{\red{QUESTION : }}}}}$

The length of a rectangle is 4 cm more than its breadth. The perimeter of the rectangle is 40 cm. Find the length and breadth of the rectangle ?

$\huge\purple{ \underline{ \boxed{\mathbb\colorbox{cyan}{\red{ANSWER : }}}}}$

Length of rectangle = 12 cm

Breadth of rectangle = 8 cm

$\huge\purple{ \underline{ \boxed{\mathbb\colorbox{cyan}{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

The length of a rectangle is 4 cm more than its breadth.

The perimeter of the rectangle is 40 cm.

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

The length and breadth of the rectangle .

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED: }}}}$

$\purple{ \boxed{ \textsf{Perimeter of rectangle = 2 \: ( L + B)}}}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

Let breadth of rectangle = x cm

Then length of rectangle = x + 4 cm

$\red{ \underline{\underline{ \textbf{According to question : }}}}$

$\textsf{Perimeter of rectangle = 2 \: ( L + B)}$

$\displaystyle \longrightarrow \bf40 \: cm = 2 \: (x + 4 + x) \\ \\ \displaystyle \longrightarrow \bf40 \: cm = 2 \: (2x + 4) \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf40 \:cm = 4x + 8 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf4x + 8 = 40 \: cm \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf4x = 40 - 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf4x = 32 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf x = \frac{32}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow \bf x = 8 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \begin{array}{l} \textsf{Breadth of rectangle = x = 8 cm}\\ \\ \textsf{Length of rectangle = x + 4 = 8 + 4 = 12 \: cm }\end{array}}}$