Question

The length of a rectangle is 2ft longer than it’s width. If the perimeter of the rectangle is 32 ft, find it’s area

Answer 1

• 63 sq.ft

⠀

Explanation:

⠀

• As it is given that, the length of a rectangle is 2ft longer than it’s width and perimeter of the rectangle is 32 ft.

⠀

So, let us assume the width of the rectangle as w ft and therefore the length will (w + 2) ft .

⠀

Now,

⠀

`{\longrightarrow \qquad{ {{\boldsymbol {2 ( Length + Breadth )= Perimeter_((Rectangle)) }}}}}`

⠀

`{\longrightarrow \qquad {\rm{2(w + 2 + {w})= 32 \ }}}`

⠀

`{\longrightarrow \qquad {\rm 2({2w + 2= 32 ) }}}`

⠀

`{\longrightarrow \qquad {\rm{4w +4= 32 \ }}}`

⠀

`{\longrightarrow \qquad {\rm{4w = 28\ }}}`

⠀

`{\longrightarrow \qquad {\rm{w = (28)/(4) }}}`

⠀

`{\longrightarrow \qquad{ \mathfrak{{\pmb{w = 7 }}}}}`

⠀

• Therefore width of the rectangle is 7 ft .

⠀

Now, We are to find the length of the rectangle:

`{\longrightarrow \qquad{ {{\rm{Length = w + 2 }}}}}`

⠀

`{\longrightarrow \qquad{ {{ \rm{Length = 7 + 2 }}}}}`

⠀

`{\longrightarrow \qquad{ { \frak{ \pmb{Length = 9}}}}}`

⠀

Now, we are to find the area of the rectangle :

⠀

`{\longrightarrow \qquad{ {{\boldsymbol{ Area_((Rectangle)) = Length * Breadth }}}}}`

⠀

`{\longrightarrow \qquad{ {{ \rm{ Area_((Rectangle)) = 9 * 7 }}}}}`

⠀

`{\longrightarrow \qquad{ { \pmb{\boldsymbol{ Area_((Rectangle)) = 63 }}}}}`

⠀

Therefore,

• The area of the rectangle is 63 ft².

⠀

Answer 2

• Area of rectangle is 63 feet²

Explanation:

Given:

• The length of a rectangle is 2ft longer than it’s width.
• If the perimeter of the rectangle is 32 ft

To Find:

• Area of the rectangle.

Solution:

Let's assume Width of rectangle be x feet and length be 2 +x. to Find the are of the rectangle firstly we need to the length and width of the Rectangle:

Using formula:

• Perimeter of rectangle = 2(L + B)

→ 32 = 2(x + 2 + x)

→ 32 = 2(2x + 2)

→ 32 = 4x + 4

→ 32 - 4 = 4x

→ 28 = 4x

→ 28/4 = x

→ 7 = x

Hence,

• Length of the rectangle = 2 + x = 9 feet
• Width of the rectangle = x = 7 feet.

Now,

→ Area of rectangle = Length × Width

→ Area fo rectangle = 9 × 7

→ Area of rectangle = 63 feet²

• Hence, Area of the rectangle is 63 feet²