Question

The width of a rectangle is two-thirds of its length.if the perimeter of the reactangle is 80m. find its area

Answer 1

Given :-

• The width of a rectangle is two-thirds of its length.if the perimeter of the reactangle is 80m.

To Find :-

• Area of rectangle

Solution :-

Let the length be x m and breadth be y m

then,

➦ According to the Question

• Perimeter of rectangle = 80m

➪ 2(length + breadth) = 80

➪2(x + 2x/3) = 80

➪ (2x + 2x/3) = 80/2

➪ 4x/3 = 40

➪ x = 40 × 3/4

➪ x = 10 × 3

➪ x = 30

Hence,

• Length of rectangle = x = 30m
• Breadth of rectangle = 2x/3= 20m

Now, area of rectangle

➪ length × breadth

➪ l × b

➪ 30 × 20

➪ 600m²

Therefore,

• Area of Rectangle = 600 m²

$\rule{200}3$

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \orange{Question:-}}}}}}$

The width of a rectangle is two-thirds of its length.if the perimeter of the Rectangle is 80m. Find its area ..

_______________

${ \huge{ \bold{ \underline{ \underline{ \red{Answer:-}}}}}}$

✒Given : -

• The width of a rectangle is two-thirds of its length...
• Perimeter of the Rectangle is 80 m ..

✒To Find : -

• Area of the Rectangle = ?

✒Formula Used : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \green{Perimeter\:of\:Rectangle=2(l+b)}}}}}}}$

✒Let ,

• Length of the rectangle = y
• Then, Breadth will be = 2y/3

✒On Substituting Values : -

$\dashrightarrow\sf{2(l+b)=80}$

$\dashrightarrow\sf{2\bigg(y+\dfrac{2y}{3}\bigg)=80}$

$\dashrightarrow\sf{2y+\dfrac{2y}{3}=\cancel\dfrac{80}{2}}$

$\dashrightarrow\sf{2y+2y=40\times{3}}$

$\dashrightarrow\sf{4y=120}$

$\dashrightarrow\sf{y=\cancel\dfrac{120}{4}}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \blue{y=30}}}}}}}$

✒Therefore , Length of Rectangle is 30m ..

✒Hence ,

$\dashrightarrow\sf{Length\:of\:Rectangle(y)=30m}$

$\dashrightarrow\sf{Breadth\:of\: rectangle(2y/3)=\dfrac{2(30)}{3}}$

$\dashrightarrow\sf{\cancel\dfrac{60}{3}}$

$\leadsto\sf\bold{20m.}$

✒Formula Used : -

$\leadsto\sf{{ \small{ \bold{ \bold{ \bold{ \pink{Area\:of\:Rectangle=l\times{b}}}}}}}}$

$\dashrightarrow\sf{30\times{20}}$

$\dashrightarrow\sf{600{m}^{2}}$

→ So , the Area of Rectangle is 600m² ..