Question

the length of a rectangle is 17cm more than its breadth. its perimeter is 134cm. find the length and breadth

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Length of the Rectangle is 42 cm and Breadth is 25 cm.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Length of the Rectangle = 17 cm more than its Breadth

Perimeter of the Rectangle = 134 cm

To Find :

The length and breadth of the Rectangle

Solution :

◆$\textbf{\small{\underline{Consider the -}}}$

• Breadth as x
• Length as x + 17

★ Perimeter = $\boxed{\sf{2(Length+Breadth)}}$

$\tt{\longrightarrow} \: 2(x +17 + x) = 134$

$\tt{\longrightarrow} \: 2x + 34 + 2x = 134$

$\tt{\longrightarrow} \: 4x + 34 = 134$

$\tt{\longrightarrow} \: 4x = 134 - 34$

$\tt{\longrightarrow} \: 4x = 100$

$\tt{\longrightarrow} \: x = \dfrac{100}{4}$

$\tt{\longrightarrow} \: x = 25$

Breadth = 25 cm

$\rule{300}{1.5}$

★ Value of x + 17

$\tt{\longrightarrow} \: 25 + 17$

$\tt{\longrightarrow} \: 42$

Length = 42 cm

$\therefore$ The Length of the Rectangle is 42 cm and Breadth is 25 cm.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\tt{\longrightarrow} \: 2(42 + 25) = 134$

$\tt{\longrightarrow} \: 84 + 50 = 134$

$\tt{\longrightarrow} \: 134 = 134$

$\therefore$ The Length of the Rectangle is 42 cm and Breadth is 25 cm.

Answer 2

• Let Breadth of rectangle be (M) cm.

» The length of a rectangle is 17cm more than its breadth.

• Length of rectangle = (M + 17) cm

• Perimeter of rectangle = 134 cm

______________ [ GIVEN ]

• We have to find the length and breadth of the rectangle.

____________________________

We know that..

Perimeter of rectangle = 2(length + breadth)

Put the known values in above formula

→ Perimeter of rectangle = 2(M + 17 + M)

Perimeter = 134 (Given)

→ 134 = 2(2M + 17)

→ 134 = 4M + 34

→ 134 - 34 = 4M

→ 100 = 4M

→ 4M = 100

→ M = 100/4

→ M = 25

______________________________

From above calculations we get M = 25

So,

Length of rectangle = M + 17

→ 25 + 17

→ 42 cm

Breadth of rectangle = M

→ 25 cm

______________________________

Length of rectangle = 25 cm and Breadth of rectangle = 42 cm

_________ [ ANSWER ]

______________________________

✡ VERIFICATION :

From above calculations we have Length = 25 and breadth = 42

And perimeter = 134 cm (given in question)

So,

Perimeter of rectangle = 2(length + breadth)

=> 134 = 2(25 + 42)

=> 134 = 2(67)

=> 134 = 134

_____________________________