Q:

If each side of a square is increased by 25%, find the percentage change in its area?

A) 65.25 B) 56.25
C) 65 D) 56
 
Answer & Explanation Answer: B) 56.25

Explanation:

let each side of the square be a , then area = a x a

As given that The side is increased by 25%, then

New side =  = 

New area = 

increased area= 

Increase %=  % = 56.25%

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143 32955
Q:

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

A) 55% B) 65%
C) 75% D) 85%
 
Answer & Explanation Answer: C) 75%

Explanation:

Let original radius = R.

New radius = 

Original area =  and new area = 

Decrease in area =  = 75%

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40 15583
Q:

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

A) 30 B) 40
C) 50 D) 60
 
Answer & Explanation Answer: A) 30

Explanation:

Let the side of the square(ABCD) be x meters.

Then, AB + BC = 2x metres.

AC =  = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % = = 30% (approx)

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24 13591
Q:

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

A) 136 B) 236
C) 336 D) 436
 
Answer & Explanation Answer: C) 336

Explanation:

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

Area of triangle ABC = \inline {\color{Black}\sqrt{s(s-a)(s-b)(s-c)}}

                                   = \inline {\color{Black}\sqrt{42(12)(28)(2)}}= 168sq m

area of parallelogram ABCD = 2 x 168 = 336 sq m

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21 9412
Q:

If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.

A) 110 B) 120
C) 130 D) 140
 
Answer & Explanation Answer: B) 120

Explanation:

let length = x and breadth = y then

2(x+y) = 46    x+y = 23

x²+y² = 17² = 289

now (x+y)² = 23²

x²+y²+2xy= 529

289+ 2xy = 529

 xy = 120

area = xy = 120 sq.cm

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28 9304