Question Detail

The sides of a triangle are in the ratio of $\begin{aligned}\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\end{aligned}$ . If the perimeter is 52 cm, then find the length of the smallest side.

12 cm
14 cm
16 cm
18 cm

Answer: Option A

Explanation:

$\begin{aligned} \text{Ratio of sides =}\frac{1}{2}:\frac{1}{3}:\frac{1}{4} \\ =6:4:3\\ Perimeter = 52 cm \\ \text{So sides are =} \\ \left( 52*\frac{6}{13}\right)cm,\left( 52*\frac{4}{13}\right)cm, \left( 52*\frac{3}{13}\right)cm \end{aligned}$
a = 24 cm, b = 16 cm and c = 12 cm
Length of the smallest side = 12 cm

1. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required ?

88 feet
86 feet
84 feet
82 feet

Answer: Option A

Explanation:

We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 680
=> Breadth = 34 feet

Area to be fenced = 2B + L = 2*34 + 20
= 88 feet

2. 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

$\begin{aligned} \text{Area of square} = \frac{1}{2}*{Diagonal}^2 \\ \frac{1}{2}*{2x}^2:\frac{1}{2}*{5x}^2 \\ 4x^2:25x^2 = 4:25 \end{aligned}$

3. The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.

9 cm
8 cm
7 cm
6 cm

Answer: Option C

Explanation:

Let the lengths of the line segments be x and x+2 cm
then,

$\begin{aligned} {(x+2)}^2 - x^2 = 32 \\ x^2 + 4x + 4 - x^2 = 32 \\ 4x = 28 \\ x = 7 cm \end{aligned}$

4. 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 =

$\begin{aligned} \frac{72}{50}m^2 = 1.44 m^2\\ \text{Length of each slab =}\sqrt{1.44} \\ = 1.2m = 120 cm \end{aligned}$

5. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

$\begin{aligned} 120m^2 \end{aligned}$
$\begin{aligned} 130m^2 \end{aligned}$
$\begin{aligned} 140m^2 \end{aligned}$
$\begin{aligned} 150m^2 \end{aligned}$

Answer: Option A

Explanation:

$\begin{aligned} \text{We know }h^2 = b^2+h^2 \\ =>\text{Other side }= \sqrt{(17)^2-(15)^2} \\ = \sqrt{289-225} = \sqrt{64} \\ = 8 meter \\ Area = Length \times Breadth \\ = 15\times8 m^2 = 120 m^2 \end{aligned}$

Question Detail

The sides of a triangle are in the ratio of $\begin{aligned}\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\end{aligned}$ . If the perimeter is 52 cm, then find the length of the smallest side.

1. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required ?

2. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

3. The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.

4. 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.

5. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

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Question Detail

The sides of a triangle are in the ratio of 12:13:14\begin{aligned}\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\end{aligned}. If the perimeter is 52 cm, then find the length of the smallest side.

1. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required ?

2. The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

3. The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.

4. 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.

5. One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

Thanks ! Your comment will be approved shortly !

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The sides of a triangle are in the ratio of $\begin{aligned}\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\end{aligned}$ . If the perimeter is 52 cm, then find the length of the smallest side.