Question

The breadth of a rectangle is two third of its length if the perimeter is 30 m find the length and the breadth of a rectangle

Answer 1

Answer:-

Let the length of the rectangle be "L".

Given:

Breadth of the rectangle = two - third of length.

→ Breadth = 2L/3

And it's Perimeter = 30 m

We know that,

Perimeter of a rectangle = 2(Length + Breadth)

$\sf →2(L+ \frac{2L}{3} ) = 30 \: m \\ \\ \sf{→2( \frac{3l + 2l}{3} ) = 30} \\ \\\sf{→ 6L + 4L = 30(3) }\\ \\\sf{→ 10L = 90} \\ \\\sf{→ L = \frac{90}{10} } \\ \\ \sf{→L = 9 \: m } \\ \\ \sf{Breadth \: = \frac{2L}{3} } \\ \\\sf{→ Breadth = \frac{2(9)}{3}} \\ \\ \sf{→Breadth \: = 6 \: m}$

Hence, the dimensions of the rectangle are 9 m and 6 m.

Answer 2

✬ Length = 9 m ✬

✬ Breadth = 6 m ✬

Step-by-step explanation:

Given:

• Breadth of rectangle is two third of its length.
• Perimeter of the rectangle is 30 m.

To Find:

• What is the measure of length & breadth of rectangle ?

Solution: Let the length of rectangle be L m.

∴ Breadth = 2/3 of Length

➯ Breadth = 2/3 $\times$ L

➯ Breadth = 2L/3 m.

As we know that -

★ Perimeter of rectangle = 2 ( Length + Breadth ) ★

But, A/q

• Perimeter = 30 m.

$\implies{\rm }$ 30 = 2 ( Length + Breadth )

$\implies{\rm }$ 30 = 2 ( L + 2L/3 ) {Take LCM }

$\implies{\rm }$ 30 = 2 ( 3L + 2L/3 )

$\implies{\rm }$ 30 = 2 $\times$ 5L/3

$\implies{\rm }$ 30 = 10L/3

$\implies{\rm }$ 30 $\times$ 3 = 10L

$\implies{\rm }$ 90 = 10L

$\implies{\rm }$ 90/10 = L

$\implies{\rm }$ 9 m = L

Hence, the Length of rectangle is L = 9 m.

∴ Breadth of rectangle = 2L/3

➟ 2 $\times$ 9/3

➟ 18/3 = 6 m.

_______________________

★ Verification ★

➬ 30 m = 2 ( L + B ) m

➬ 30 m = 2 ( 9 + 6 ) m

➬ 30 m = 2 (15) m

➬ 30 m = 30 m

[ Verified ]