If the length of the diagonal of a square is 20cm, | Area Questions & Answers

Q:

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

A) 2520	B) 2420
C) 2320	D) 2620

Answer & Explanation Answer: A) 2520

Explanation:

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) = 2520 sq.m

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Q:

What is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad?

A) 814	B) 714
C) 614	D) 713

Answer & Explanation Answer: A) 814

Explanation:

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.

Area of each tile = $(41 \times 41) c m^{2}$

Required number of tiles = $\frac{1517 \times 902}{41 \times 41}$ = 814

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Q:

The diagonal of a rectangle is $\sqrt{41}$ cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

A) 18	B) 28
C) 38	D) 48

Answer & Explanation Answer: A) 18

Explanation:

$\sqrt{(l^{2} + b^{2})} = \sqrt{41}$ (or) $l^{2} + b^{2} = 41$

Also, $l b = 20$

${(l + b)}^{2} = l^{2 +} b^{2} + 2 l b$ = 41 + 40 = 81

(l + b) = 9.

Perimeter = 2(l + b) = 18 cm.

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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 = $\sqrt{2 x}$ = (1.41x) m.

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

Saving % = $\frac{0.59 x}{2 x} * 100$ = 30% (approx)

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Q:

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

A) 18%	B) 28%
C) 38%	D) 48%

Answer & Explanation Answer: B) 28%

Explanation:

Let original length = x and original breadth = y.

Decrease in area = xy - $(\frac{80}{100} x \times \frac{90}{100} y)$ = (7/25)xy

Decrease % = (7/25)xy * (1/xy) * 100 = 28%

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Q:

The diagonal of the floor of a rectangular closet is 7 $\frac{1}{2}$ feet. The shorter side of the closet is 4 $\frac{1}{2}$ feet. What is the area of the closet in square feet?

A) 9	B) 18
C) 27	D) 36

Answer & Explanation Answer: C) 27

Explanation:

Other side = $\sqrt{d^{2} - s^{2}}$ = $\sqrt{(\frac{225}{4} - \frac{81}{4})}$ = $\sqrt{\frac{144}{4}}$ = 6 ft

Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

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Q:

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: C) 3

Explanation:

Area of the park = (60 x 40) = 2400 $m^{2}$

Area of the lawn = 2109 $m^{2}$

Area of the crossroads = (2400 - 2109) = 291 $m^{2}$

Let the width of the road be x metres. Then,

$60 x + 40 x - X^{2} = 291$

$x^{2} - 100 x + 291 = 0$

(x - 97)(x - 3) = 0
x = 3.

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Q:

The percentage increase in the area of a rectangle, if each of its sides is increased by 20%

A) 22%	B) 33%
C) 44%	D) 55%

Answer & Explanation Answer: C) 44%

Explanation:

Let original length = x metres and original breadth = y metres.

Original area = xy sq.m

Increased length = $\frac{120}{100}$ and Increased breadth = $\frac{120}{100}$

New area = $\frac{120}{100} x * \frac{120}{100} y = \frac{36}{25} x y m^{2}$

The difference between the Original area and New area is:

$\frac{36}{25} x y - x y$

$\frac{11}{25} x y$ Increase % = $(\frac{\frac{11}{25} x y}{x y}) * 100$ = 44%

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A) a	B) b
C) c	D) d

If the length of the diagonal of a square is 20cm,then its perimeter must be

a. $40 \sqrt{2}$ cm b. $30 \sqrt{2}$ cm c. 10cm d. 15 $\sqrt{2}$ cm

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If the length of the diagonal of a square is 20cm,then its perimeter must be a. 402cm b. 302cm c. 10cm d. 152cm

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If the length of the diagonal of a square is 20cm,then its perimeter must be

a. $40 \sqrt{2}$ cm b. $30 \sqrt{2}$ cm c. 10cm d. 15 $\sqrt{2}$ cm