ss3617 wrote:

In the given figure, ABCD is a rectangle. P and Q are midpoints of the side CD and BC respectively. Then the ratio of area of shaded region to non shaded one is?

A. 5:4

B. 4:3

C. 5:3

D. 8:3

E. 3:5

As values of sides of rectangle is not given and we need to calculate the ratio, we can assume Smart numbers for easy calculation.

Let length of rectangle \(AB=DP=40\) and width \(AD=BC=20\)

Hence area of rectangle \(= 40*20=800\)

Area of non-shaded region \(= 800-\)area of shaded region

so \(DP=PC=20\) and \(BQ=CQ=10\)

Now its easy to calculate areas of shaded regions which are right angle triangles ADP, CPQ and ABQ

the area of ADP\(=\frac{1}{2}*20*20=200\)

area of CPQ\(= \frac{1}{2}*20*10=100\)

area of ABQ\(=\frac{1}{2}*40*10=200\)

Hence area of shaded region \(= 200+200+100=500\)

area of non shaded region \(= 800-500=300\)

So ratio \(= \frac{500}{300}=5:3\)

Option

C