Question

The ratio of length and width of a door is 5:3 and its perimeter is 48m. Find the measurement of door

Answer 1

Answer:

• 135m²

Explanation:

A door with ratio of,

• length : width = 5 : 3

And also, the perimeter is 48m

Let's say that,

• length = 5x
• width = 3x

Then, the perimeter will be :-

⇒ 2(length + width)

⇒ 2(5x + 3x)

⇒ 2(8x)

⇒ 16x

But, the perimeter given is 48m

According to the question,

⇒ 16x = 48

⇒ x = 48/16

⇒ x = 3

Therefore,

• Length = 5x = 5(3) = 15m
• Width = 3x = 3(3) = 9m

Hence, it's measurement is :-

⇒ length × width

⇒ 15 × 9

⇒ 135m²

∴ Measurement of the door is 135m²

_________________________

Answer 2

$\large \tt \green{ \pmb{ \underline{Given : }}}$

• The ratio of length and width of a door is 5 : 3.
• It's perimeter is 48 m.

$\large \tt \green{ \pmb{ \underline{To \: find : }}}$

• Find the measurement of door.

$\large \tt \green{ \pmb{ \underline{Solution : }}}$

$\sf{ let \: consider \: that \: common \: number \: be \: x.}$

$\sf{ \therefore \: length \: = 5x}$

$\sf{breadth = 3x}$

$\sf{We \: know \: that,}$

$\sf{The \: shape \: of \: door \: is \: rectangle}$

$\fbox{ \sf\color{pink}{ \underline{Perimeter \: of \: rectangle = 2(length + breadth)}}}$

$\sf{ \qquad \: \: \: \dashrightarrow \: 48 = 2(5x + 3x)}$

$\sf{ \qquad \: \: \: \: \: \dashrightarrow \: 48 = 2 \times 8x}$

$\sf{ \qquad \: \: \: \: \: \: \: \dashrightarrow \: 48 = 16x}$

$\sf{ \qquad \: \: \: \: \: \: \: \: \: \dashrightarrow \: x = \cancel{ \frac{48}{16} }}$

$\sf{ { \qquad \: \: \: \: \: \: \: \: \: \: \: \dashrightarrow \underline \color{greenyellow}{ \: x = 3}}}$

$\sf{ \: \: \: \: \ \:────┈┈┈┄┄╌╌╌╌┄┄┈┈┈──── }$

$\sf{length = 5x = 5 \times 3 = 15}$

$\sf{breadth = 3x = 3 \times 3 = 9}$

$\sf{ \therefore \: Measurement = Length \times breadth}$

$\sf{ \qquad \: \: \: \: \dashrightarrow \: Measurement = 15 \times 9 = 135 {m}^{2} }$