Question

the length of a rectangle is three times as long as its breadth if its perimeter is 56 find the area of the rectangle​

Answer 1

Correct Question -:

The length of a rectangle is three times as long as its breadth if its perimeter is 56 m find the area of the rectangle.

Explanation -:

Given :

• Length of a rectangle is three times it's breadth
• Perimeter of a rectangle = 56m

To Find :

• Area of the rectangle

Solution :

Length of a rectangle is three times its breadth

Let the breadth be x

Then, Length = 3x

$\small\rm{Perimeter \: of \: a \: rectangle = 2(Length + Breadth)}$

Perimeter = 56 m

$\small\rm \bf{56 = 2(3x + x)}$

$⇢ \small\rm{56 = 2(4x)}$

$⇢ \small\rm{56 = 8x}$

$⇢ \small\rm{ \dfrac{ \cancel{56}} { \cancel{8}} = x}$

$⇢ \small\rm{ \fbox{ x = \: 7 }}$

Now putting the value of x = 7 in length and breadth

Length = 3x = 3 × 7 = 21 m

Breadth = x = 7m

Area of a rectangle

Length = 21 m

Breadth = 7 m

$\small\rm{Area \: of \: a \: rectangle = length \times breadth}$

$\small\rm \bf{Area \: = (21 \times 7}) {m}^{2}$

$\small\rm{Area = 147 {m}^{2} }$

Area of the rectangle = 147 m²

$\underline{ \rule{70mm}{3pt}}$

Answer 2

Revised Question : -

the length of a rectangle is three times as long as its breadth if its perimeter is 56 metres. find the area of the rectangle.

$\sf\purple{\underline{Answer:-}}$

Given :

• Length is thrice the breadth
• Perimeter = 56 m

Let the breadth be x and the length be 3x

Now,

$\mathfrak\orange{Perimeter\:=\:56m}$

➻ 56 m = 2(x + 3x)

➻ $\frac{56}{2}$ = 4x

➻ 28 = 4x

➻ $\frac{28}{4}$ = x

➻ x = 7 m

Therefore, 3x = 3*7 = 21 m

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$\sf\purple{ Final\:Answer}$

• Length = 21 m
• Breadth = 7 m

$\underline{\rule{220pt}{3pt}}$