Question

15. If the length of a rectangle is 3 times to its breadth and the perimeter of the rectangle is 32 units, then find the breadth of the rectangle.​

Answer 1

Answer:

Breadth of the rectangle is 4 units.

Explanation:

Given,

Length of a rectangle is 3 times the breadth.

If we assume the length as ‘x’

Then, breadth will be ‘3x’

We know,

Perimeter of a rectangle = 2(l + b)

Where, l is the length and b is breadth.

According to the question,

Perimeter is 32 units.

Then,

→ 2(l + b) = 32

→ 2(3x + x) = 32

→ 6x + 2x = 32

→ 8x = 32

→ x = 32/8

→ x = 4

∴ x = 4 units

Hence,

• breadth = x = 4 units.
• Length = 3x = 3(4) = 12 units.

_____________________

Formula used:

Perimeter of a rectangle = 2(l + b)

Where, l denotes the length and b is the breadth.

Answer 2

Given :

If the length of a rectangle is 3 times to its breadth and the perimeter of the rectangle is 32 units, then find the breadth of the rectangle.

Solution :

Let us assume :

The Breadth be taken as B

Then, according to the question

Length will be 3 times of breadth which can taken as 3B

Formula for Perimeter :

$\: \: \: \: \: \: \: \: \: \: \: \star \: \red{ \underline{ \overline{ \pink{ \boxed{ \orange{\frak{{ \sf P}erimeter_{{( \sf R}ectangle)} = 2( Length + Breadth)}}}}}}}$

Putting the values according to the formula we get :

$\dashrightarrow \sf{32 \: units = 2(B + 3B)}$

$\dashrightarrow \sf32 \: units = 2(4B )$

$\dashrightarrow \sf32 \: units = 8B$

By cross multiplying we get :

$\dashrightarrow \sf B = \frac{32}{8} \: units$

$\dashrightarrow \sf B = \cancel{ \frac{32}{8} } \: units$

$\star \: \green{\underline{ \overline{ \orange{\boxed{ \blue{ \sf B = 4\: units}}}}}}$

__________________________

Now, finding the Length and Breadth

Breadth = B = 4 units

Length = 3B = 3 × 4 units = 12 units

☬ The Breadth is 4 units whereas the Length is 12 units

Verification :

Using the same formula we can verify it

• Perimeter = 2(Length+ Breadth)

• 32 units = 2(12 units + 4 units)

• 32 units = 2(16 units)

• 32 units = 32 units

HENCE, VERIFIED ✓✓