Question

if breadth of a rectangle in three fourths of its length and perimeter is 140 am,find the length and breadth of the rectangle.

Answer 1

Answer:-

Length = 40cm

Breadth = 30cm

Explanation:-

Given:

breadth of rectangle is 3/4th of its length

Perimeter of rectangle = 140cm

To Find:-

Length and breadth of triangle

Solution:-

let,

• length of triangle is x
• breadth of triangle is 3x/4

Now,

Perimeter of rectangle = 2(l+b)

${\rightarrow}2(x + \dfrac{3x}{4}) = 140$

${\rightarrow}2( \dfrac{4x+ 3x}{4}) = 140$

${\rightarrow} \dfrac{7x}{2} = 140$

${\rightarrow} 7x = 280$

${\rightarrow} x = 40$

$\bold{Length= 40cm}$

Now,

${\rightarrow}breadth = \dfrac{3x}{4}$

${\rightarrow}b= \dfrac{3(40)}{4}$

${\rightarrow}b= \dfrac{120}{4}$

${\rightarrow}b= 30$

$\bold{breadth = 30cm}$

Verification:-

${\rightarrow}2(l+b)= 140$

${\rightarrow}2(40+30)= 140$

${\rightarrow}2(70)= 140$

${\rightarrow}140=140$

Hence, length and breadth of rectangle are 40cm and 30cm respectively.

Answer 2

Answer :-

Length and breadth of the rectangle are 40 cm and 30 cm respectively.

Explanation :-

Let the length of the rectangle be 'x' cm

Breadth of the rectangle = three - fpurth of the length = (3/4) * x = 3x/4 cm

Given

Perimeter of the rectangle = 140 cm

Also

Perimeter of the rectangle = 2(l + b)

$\\ \mathsf{ \implies 140 = 2 \bigg( x + \dfrac{3x}{4} \bigg)} \\ \\ \\ \mathsf{ \implies 140 = 2 \bigg( \dfrac{4x + 3x}{4} \bigg) } \\ \\ \\ \mathsf{ \implies 140 = 2 \bigg( \dfrac{7x}{4} \bigg) } \\ \\ \\ \mathsf{ \implies 140 = \dfrac{7x}{2} } \\ \\ \\ \mathsf{ \implies 140(2) = 7x} \\ \\ \\ \mathsf{ \implies 280 = 7x} \\ \\ \\ \mathsf{ \implies \dfrac{280}{7} = x} \\ \\ \\ \mathsf{ \implies 40 = x} \\ \\ \\ \mathsf{ \implies x = 40}$

Length of the rectangle = x = 40 cm

Breadth of the rectangle = 3x/4 = 3(40)/4 = 3(10) = 30 cm

∴ Length and breadth of the rectangle are 40 cm and 30 cm respectively.