Question

The width of a rectangle is two - thirds its length . if the perimeter is 180 cm find its dimensions

Answer 1

Answer:

The dimensions, "length and width" of the rectangle are 54 cm and 36 cm.

Solution:

Let the "length" of the rectangle be l.

Given, the "width" of a rectangle is "two - thirds its length".

So, the width of the rectangle  

$= \frac { 2 } { 3 } \times l = \frac { 2 } { 3 } l$

Given, Perimeter of the rectangle = 180 cm.

We know,  

Perimeter of a rectangle = 2 (length + width) = 180 cm

$\begin{array} { c } { 2 \left( l + \frac { 2 } { 3 } l \right) = 180 \mathrm { cm } } \\\\ { 2 \left( \frac { 3 + 2 } { 3 } l \right) = 180 \mathrm { cm } } \\\\ { 2 \times \frac { 5 } { 3 } l = 180 \mathrm { cm } } \\\\ { \frac { 10 } { 3 } l = 180 \mathrm { cm } } \\\\ { l = \frac { 180 \times 3 } { 10 } \mathrm { cm } } \\\\ { l = 54 \mathrm { cm } } \end{array}$

Hence, Length = l = 54 cm.

So, Width  

$= \frac { 2 } { 3 } l = \frac { 2 } { 3 } \times 54 c m = 36 \mathrm { cm }$

Thus, the dimensions, "length and width" of the rectangle are 54 cm and 36 cm.

Answer 2

Answer:

the "width" of a rectangle is "two - thirds its length". Given, Perimeter of the rectangle = 180 cm. Hence, Length = l = 54 cm. Thus, the dimensions, "length and width" of the rectangle are 54 cm and 36 cm.