Problem 1: The ratio of three angles of a quadrilateral are in the ratio 1: 6 : 2. The measure of fourth angle is 450. What is the difference between the largest and smallest angle?

Solution:

Sum of four angles in a quadrilateral is 360

x+6x+2x+45 = 360

9x = 315

x = 35

Difference between smallest and largest angle is 6x-x = 5x

5x = 5*35 = 175

Problem 2: On increasing the diameter of a circle by 75 %, what will be the percentage increase in the perimeter?

Solution:

If radius is increased perimeter is also increase.

75%=

actual diameter increased diameter

4 7

16 49

%

Problem 3: If the longer side of a rectangle is doubled and the other reduced to half, then find what will be the percentage increment in the area of the new rectangle?

Solution:

Let length =10 breadth = 10 ——->10*10=100

double length =20 half breadth=5——->20*5=100

no increment in the area 0%