The sides of a rectangle are in the ratio 4 : 5 and its perimeter is 90 cm.Find the dimensions of the rectangle and hence its area.

Question

The sides of a rectangle are in the ratio 4 : 5 and its perimeter is 90 cm.Find the dimensions of the rectangle and hence its area.

Answer 1

Hi Santhosh,

We know that the sum of the lengths of all sides of your rectangle are equal to 90 and that the sides have a ratio of 4:5.  We can solve this using simple algebra.

Lets say the shorter side is 4x in length and the longer side is 5x based on the ratio given in the problem.

For all rectangles, perimeter=2(length)+2(width)

So if we substitute the x values we assigned above, we get 2(4x)+2(5x)=90

We can simplify this equation:

8x+10x=90

18x=90

Then divide both sides by 18 to solve for x;

x=5.

 

If shorter side = 4x, and x =5, the width is 4*5 = 20cm

If longer side = 5x and x=5, the length is 5*5 = 25cm

 

For all rectangles, Area=length x width

Using the values we calculated above:

Area = 20cm x 25cm = 500cm

 

Thanks

Beth