Question

10. The area of a square is 225 m². The perimeter of the square is 10 m less than the perimeter of the
rectangle and breadth of the rectangle is 15 m. Find the area of the rectangle is m2
a) 150
b) 350
c) 300
d) 75​

Answer 1

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

Option c) 300 m²

The area of the Rectangle is 300 m².

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

Given :

Area of the Square = 225 m²

Perimeter of Square = 10 less than Perimeter of Rectangle

Breadth of the Rectangle = 15 m

To find :

The area of the Rectangle

Solution :

First find the side of the Square. We can find it as we are given with the area of the Square.

★ $\boxed{\sf{Area \: = Side \times Side}}$

Consider side as x

$\tt{\implies} \: 225 = x \times x$

$\tt{\implies} \: x = \sqrt{225}$

$\tt{\implies} \: x = 15$

Side of the Square = 15 m

$\rule{300}{1.2}$

Find the Perimeter of Square.

★ $\boxed{\sf{Perimeter \: = Side \times 4}}$

$\tt{\implies} \: 15\times 4$

$\tt{\implies} \:60$

The Perimeter of Square = 60 m

$\rule{300}{1.2}$

It is mentioned in the question that, the Perimeter of Square is 10 less than the Perimeter of Rectangle.

So,

Perimeter of Rectangle = 60 + 10 = 70

$\boxed{\sf{Perimeter\:of\: Rectangle = 70\:m}}$

$\rule{300}{1.2}$

As We got the Perimeter of Rectangle, We can now get the Length of the Rectangle.

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

Consider Length as x

$\tt{\implies} \: 2(15 + x) = 70$

$\tt{\implies} \: 30 + 2x = 70$

$\tt{\implies} \: 2x = 70 - 30$

$\tt{\implies} \: 2x = 40$

$\tt{\implies} \: x = \dfrac{40}{2}$

$\tt{\implies} \: x = 20$

Length of the Rectangle is 20 m.

$\rule{300}{1.2}$

Find the area of Rectangle

★ $\boxed{\sf{Area=Length \times Breadth}}$

$\tt{\implies} \: 20 \times 15$

$\tt{\implies} \: 300 \: {m}^{2}$

$\therefore$ The area of the Rectangle is 300 m².

Answer 2

Solution :

Given,

Area of Square = 225 m²

Let the length of the rectangle be l.

Breadth of the rectangle, b = 15 m.

$\boxed{\mathsf{\green{Perimeter \:of\: rectangle \:= \:2(\: l\: +\: b\:)}}}$

Perimeter of rectangle = 2 ( l + 15 ) m.

Now, In Square,

$\boxed{\mathsf{\green{Area\: of \:Square \:=\:{( \:side\:)}^{2}}}}$

Let the side of Square be a.

$\mathsf{{a}^{2} \:=\: 225}$

$\mathsf{a\: =\:{\sqrt{225}\:m^2}}$

$\mathsf{a\: =\:15\:m^2}$

Now, $\boxed{\mathsf{\green{Perimeter \:of \:Square \:= \:4a}}}$

Perimeter of Square = 4* 15 m

Perimeter of Square = 60 m.

According to the question,

Perimeter of Square is 10 m less than the Perimeter of rectangle.

2 ( l + 15 ) - 60 = 10

2l + 30 - 60 = 10

2l - 30 = 10

2l = 10 + 30

2l = 40

l = 40/2 = 20 m

l = 20 m

Now, $\boxed{\mathsf{\green{Area \:of \:rectangle \:=\: l \:*\: b}}}$

Area of rectangle = 20 × 15 m²

⛛ $\boxed{\mathsf{\red{Area\: of \:rectangle\: = \:300 {m}^{2}}}}$