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Q:

In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

A) 13:9	B) 16:9
C) 15:9	D) 14:9

Answer & Explanation Answer: B) 16:9

Explanation:

Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then, $\frac{\frac{1}{2} \times x \times 3 h}{\frac{1}{2} \times y \times 4 h} = \frac{4}{3} \Rightarrow \frac{x}{y} = \frac{4}{3} \times \frac{4}{3} = \frac{16}{9}$

Required ratio = 16 : 9.

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Q:

Find the length of the altitude of an equilateral triangle of side $3 \sqrt{3}$ cm.

A) 4.5	B) 3.5
C) 2.5	D) 6.5

Answer & Explanation Answer: A) 4.5

Explanation:

Let the length of the altitude be h.
Then, h = $a \frac{\sqrt{3}}{2}$ = $3 \sqrt{3} \times \frac{\sqrt{3}}{2}$ = 4.5

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Q:

The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.

A) 4:25	B) 3:25
C) 3:15	D) 5:25

Answer & Explanation Answer: A) 4:25

Explanation:

Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = $\frac{1}{2} * {(2 x)}^{2} : \frac{1}{2} * {(5 x)}^{2} = 4 : 25$

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Q:

A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:

A) rs.458	B) rs,558
C) rs.658	D) rs.758

Answer & Explanation Answer: B) rs,558

Explanation:

Area to be plastered= [2(l + b) x h] + (l x b)

= [2(25 + 12) x 6] + (25 x 12)

= (444 + 300)

= 744 sq.m

Cost of plastering = Rs.744 x (75/100)

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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:

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 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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