Question

the perimeter of a rectangle is 52 cm if its width is 2 cm more than one third of its length,find the denominator of the rectangle​

Answer 1

$\huge \mathfrak \red{answer}$

____________________________

Question:

the perimeter of a rectangle is 52 cm if its width is 2 cm more than one third of its length,find the denominator of the rectangle

_________________________________

step by step explanation:

Given perimeter of rectangle is 52cm

let,

• length be x
• breadth is
• $\sf{ \frac{1}{3}x + 2}$

Do you know perimeter formula?

$\bf{ \boxed{ \green{ \tt{perimeter \: of \: rectangle = 2(l + b \: }}}}$

_____________________________

problem solving:

➷$\sf{2( \frac{x + 1}{3x + 2}) = 52}$

➷$\sf{2( \frac{4x}{3 + 2}) = 52}$

➷$\sf{2(( \frac{4x + 6}{3}) = 52}$

➷$\sf{ \frac{(8x + 12)}{3} = 52}$

➷$\sf{8x + 12 = 52 \times 3}$

➷$\sf{8x + 12 = 156}$

➷$\sf{8x = 156 - 12}$

➷$\sf{8x = 144}$

➷$\sf{x = \frac{144}{8}}$

➷$\sf{x = 18}$

____________________________

then

length is x = 18

breadth is

$\sf{ \frac{1}{3}x + 2}$

$\sf{ \frac{1 \times 18}{3 + 2}}$

$\sf{ = 8}$

_________________________

finally

• length is x = 18
• breadth is x= 8

________________________________

Now area of rectangle

$\bf{ \boxed{ \green{ \tt{area \: of \: rectangle = (l \times b)sq.unit \: }}}}$

$= \rm{(18 \times 8) {cm}^{2}}$

$\rm{ = 144 {cm}^{2}}$

Area of rectangle is

$\sf{144 {cm}^{2}}$

I hope it's help uh