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Question Detail
50 square stone slabs of equal size were needed to cover a floor area of 72 sq.m. Find the length of each stone slab.
- 110 cm
- 116 cm
- 118 cm
- 120 cm
Answer: Option D
Explanation:
Area of each slab =
\begin{aligned}
\frac{72}{50}m^2 = 1.44 m^2\\
\text{Length of each slab =}\sqrt{1.44} \\
= 1.2m = 120 cm
\end{aligned}
1. If the area of a square with the side a is equal to the area of a triangle with base a, then the altitude of the triangle is.
- a
- a/2
- 2a
- None of above
Answer: Option C
Explanation:
\begin{aligned}
\text{We know area of square =}a^2 \\
\text{Area of triangle =}\frac{1}{2}*a*h \\
=> \frac{1}{2}*a*h = a^2 \\
=> h = 2a
\end{aligned}
2. If the radius of a circle is diminished by 10%, then the area is diminished by:
- 200%
- 210%
- 300%
- 310%
Answer: Option C
Explanation:
Let the original radius be R cm. New radius = 2R
\begin{aligned}
Area = \pi R^2 \\
\text{New Area =} \pi {2R}^2 \\
= 4\pi R^2 \\
\text{Increase in area =}(4\pi R^2 - \pi R^2) \\
= 3\pi R^2 \\
\text{Increase percent =} \frac{3\pi R^2}{\pi R^2}*100 \\
= 300 \%
\end{aligned}
3. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.
- 4:25
- 4:15
- 3:25
- 3:15
Answer: Option A
Explanation:
Let the diagonals of the squares be 2x and 5x.
Then ratio of their areas will be
\begin{aligned}
\text{Area of square} = \frac{1}{2}*{Diagonal}^2 \\
\frac{1}{2}*{2x}^2:\frac{1}{2}*{5x}^2 \\
4x^2:25x^2 = 4:25
\end{aligned}
4. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is.
- 200 m
- 150 m
- 148 m
- 140 m
Answer: Option A
Explanation:
Let the triangle and parallelogram have common base b,
let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then
\begin{aligned}
\text{Area of triangle =}\frac{1}{2}*b*h1\\
\text{Area of rectangle =}b*h2\\
\text{As per question }\\
\frac{1}{2}*b*h1 = b*h2 \\
\frac{1}{2}*b*h1 = b*100 \\
h1 = 100*2 = 200 m \\
\end{aligned}
5. 50 square stone slabs of equal size were needed to cover a floor area of 72 sq.m. Find the length of each stone slab.
- 110 cm
- 116 cm
- 118 cm
- 120 cm
Answer: Option D
Explanation:
Area of each slab =
\begin{aligned}
\frac{72}{50}m^2 = 1.44 m^2\\
\text{Length of each slab =}\sqrt{1.44} \\
= 1.2m = 120 cm
\end{aligned}
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