Question

Find
The ratio of the length to the perimeter of a rectangle
is 3:8. Find its dimensions, given that its perimeter is
32 m. Also, find its area.​

Answer 1

Answer:

• Length of rectangle = 12cm.
• Breadth of rectangle = 4cm.
• Area of rectangle = 48 sq.m.

Step-by-step explanation:

Given:

• The ratio of the length of the perimeter of rectangle is 3:8.
• The perimeter of rectangle is 32m.

To Find:

• The dimensions and area of rectangle.

Solution:

Let length be 3x and perimeter be 8x.

=> 8 x = 32cm

=> x = 32/8

=> x = 4cm

Therefore, Length of rectangle = 3x = 12cm.

We know that,

Perimeter of rectangle = 2(length + breadth).

=> 2(12 + b) = 32cm

=> 24 + 2b = 32cm

=> 2b = 32 - 24

=> 2b = 8

=> b = 8/2

=> b = 4cm

∴ Therefore, Breadth of the rectangle is 4cm.

Now,

Area of rectangle = Length × Breadth

=> Area = 12 × 4

=> Area = 24 sq.cm

∴ Therefore, Area of rectangle is 48 sq.cm.

Answer 2

Given:

• perimeter of rectangle = 32 m

• Length and perimeter are in ratio of 3:8

To find:

• Length of rectangle

• Breadth of rectangle

• Area of rectangle

Let:

• Length of rectangle be 3x

• Perimeter of rectangle be 8x

Solution:

First of all let's find value of x

We know perimeter of rectangle is 32 m and we have supposed perimeter of rectangle as 8x

$\therefore\underline{\textsf{Equation formed according to question}}$

$\leadsto \sf32 = 8x$

$\leadsto \sf \dfrac{32}{8} = x$

$\leadsto \sf \dfrac{8 \times 4}{8} = x$

$\leadsto \sf \dfrac{ \cancel8 \times 4}{ \cancel8} = x$

$\leadsto \sf 4 \times 1= x$

$\leadsto \sf 4 = x$

$\leadsto \sf x = \textsf{ \textbf{4m}}$

∴Value of x = 4m

Now Let's find Length of rectangle:

$\longrightarrow\sf{}Length \: of \: rectangle = 3x$

$\longrightarrow\sf{}Length \: of \: rectangle = 3 \times 4$

$\longrightarrow\sf{}Length \: of \: rectangle = \textsf{ \textbf{12m}}$

∴Length of rectangle = 12 m

Now Let's find breadth of rectangle:

$\bigstar \boxed{ \rm{}perimeter \: of \: rectangle = 2(length + breadth)}$

By using this formula we can find breadth of rectangle:

$\longrightarrow\sf{}perimeter \: of \: rectangle = 2(length + breadth)$

$\longrightarrow\sf{}32 = 2(12+ breadth)$

$\longrightarrow\sf{}32 = 2(12)+ 2(breadth)$

$\longrightarrow\sf{}32 = 24+ 2(breadth)$

$\longrightarrow\sf{}32 - 24= 2(breadth)$

$\longrightarrow\sf{}8= 2(breadth)$

$\longrightarrow\sf{} \dfrac{8}{2} =breadth$

$\longrightarrow\sf{} \dfrac{2 \times 4}{2} =breadth$

$\longrightarrow\sf{} \dfrac{\cancel2 \times 4}{\cancel2} =breadth$

$\longrightarrow\sf{} 4 =breadth$

$\longrightarrow\sf{}breadth \: of \: rectangle = \bf4 \: m$

∴Breadth of rectangle = 4 m

Finally Let's find area of rectangle:

we know:

$\bigstar \boxed{ \rm{}Area \: of \: rectangle =length \times breadth}$

By using this formula we can find area of rectangle

$\dashrightarrow \sf{}Area \: of \: rectangle =12 \times 4$

$\dashrightarrow \sf{}Area \: of \: rectangle =\textsf{\textbf{48 m ^2 }}$

∴Area of rectangle = 48m²