Question

The ratio of the length of a rectangle to its breadth is 3:2. The perimeter of the rectangle is 50 cm. What is the length of the rectangle?

Answer 1

$\huge { \fbox{\sf{\underline{answer}}}} \rightarrow$

$\large \sf \green{ \underline{given : }}$

• The ratio of the length of a rectangle to its breadth is 3:2.

• The perimeter of rectangle is 50 cm.

$\large \sf \green{ \underline{to \: find : }}$

• What is the length of rectangle..??

$\large \sf \green{ \underline{solution : }}$

$\sf{let \: the \: common \: no. \: be \: x}$

$\sf{ \therefore \: length = 3x \: and \: breadth = 2x}$

$\large \sf \: we \: know \: that$

$\boxed { \sf\red{perimetre \: of \: rectangle = \: 2 \: (length + breadth)}}$

$\sf{ \qquad : \implies \: 50 = 2(3x + 2x)}$

$\sf{ \qquad : \implies \: 50 = 2 \times 5x}$

$\sf{ \qquad : \implies \: 50 = 10x}$

$\sf{ \qquad : \implies \: x = \frac{ \cancel{ {50}} \: \: ^{5} }{ \cancel{10} }}$

$\sf{ \qquad : \implies \: x = 5}$

______________________________________

$\sf{ \therefore \: length \: of \: rectangle \: = 3x}$

$\sf{ \therefore \: length \: = 3 \times 5 = 15}$

$\sf{ \therefore \: the \: length \: of \: rectangle \: is \: 15.}$