Mensuration Part 3

Problem 1: The ratio of three angles of a quadrilateral are in the ratio 1: 6: 2. The measure of the 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 the radius is increased perimeter is also increases.

75%=\frac{3}{4}

Actual diameter        Increased diameter

4                                           7

16                                        49

\frac{33}{16}\times 100=87.5%

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.

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