Question

Wraith of a rectangle is 2/3 of its length if the perimeter is 180 find dimension of the rectangle

Answer 1

Correct Question :-

Width of a rectangle is 2/3 of its length. If the perimeter is 180m , then find dimensions of the rectangle.

Solution :-

Let the length be x.

Let the length be x.Width = 2/3x

According To The Question :-

$\star{\boxed{\sf{Perimeter\ of\ rectangle\ =\ 2 (l + b)}}}$

$\rightarrow{\sf{180 = 2 (x + \dfrac{2}{3}x)}}$

$\rightarrow{\sf{180 = 2 ( \dfrac{3x + 2x}{3})}}$

$\rightarrow{\sf{180 = 2 (\dfrac{5x}{3})}}$

$\rightarrow{\sf{180 = \dfrac{10x}{3}}}$

$\rightarrow{\sf{180 \times 3 = 10x}}$

$\rightarrow{\sf{\dfrac{540}{10} = x}}$

$\rightarrow{\boxed{\sf{x = 54}}}$

So, the length is 54 m ;

Width = 36 m.

Verification :-

$\sf{Perimeter\ of\ rectangle\ = 2 (54 + 36)}$

$\rightarrow{\sf{2 (90)}}$

$\rightarrow{\sf{180 m = L.H.S.}}$

Hence, Verified !!

$\boxed{\boxed{\sf{Length = 54 m}}}$

$\boxed{\boxed{\sf{Breadth = 36 m}}}$

Answer 2

Answer

Let length = l

Width = 2/3 l

Perimeter = 2(l + b)

=> 180 = 2 (l + 2/3 l)

=> 90 = 5l/3

=> l = 54

b = 2/3 × 54

=> b = 36