Question

The perimeter of a rectangle in 120 cm. The ratio of length and its breadth in 3:2. Find the length and breadth of the rectangle

Answer 1

Answer:

Length=36cm and Breadth=24cm

Answer 2

$\bf{\huge{\underline{\boxed{\sf\purple{Answer:Length=36;Breadth=24}}}}}$

$\huge\underline{\underline{\tt Explanation:}}$

$\sf{\blue{\underline{Given:}}}$

• Perimeter of a rectangle is 120 cm.
• Ratio of length and breadth is 3 : 2

$\sf{\blue{\underline{To\:Find:}}}$

• Length and breadth of the rectangle.

$\textbf{\underline{\underline{Solution:}}}$

Opposite sides of rectangle are equal. So, The perimeter of rectangle is twice of it's one length and breadth.  

→ Perimeter of rectangle = 2 ( length and breadth )

Let the common factor in their ratios be ' x '

So,

→ Length = 3x

→ Breadth = 2x

Now,

$\textsf{\underline{\large{According\:to\:Question:}}}$

2 ( 3x + 2x ) = 120

→ 2 ( 5x ) = 120

→ 10x = 120

→ $x = \dfrac{120}{10}$

∴ x = 12

Vale of ' x ' is 12.

→ Put the value of ' x ' in length and breadth.

we get,

→ Length = 3 × 12 = 36 cm

→ Breadth = 2 × 12 = 24 cm

$\huge\star\underline\mathscr\green{Verification:}$

Perimeter of Rectangle = 120 cm

So,

2 ( length + breadth ) = 120

→ 2 ( 36 +  24 ) = 120

→ 2 ( 60 ) = 120

→ 120 = 120

L.H.S = R.H.S

Hence, Proved!