Question Detail

A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

10 m * 5 m
15 m * 5 m
20 m * 5 m
25 m * 5 m

Answer: Option C

Explanation:

From the question, 2b+l = 30
=> l = 30-2b

$\begin{aligned} Area = 100m^2 \\ => l \times b = 100 \\ => b(30-2b) = 100 \\ b^2 - 15b + 50 = 0 \\ =>(b-10)(b-5)=0 \\ \end{aligned}$
b = 10 or b = 5
when b = 10 then l = 10
when b = 5 then l = 20
Since the garden is rectangular so we will take value of breadth 5.
So its dimensions are 20 m * 5 m

1. The length of a rectangle is three times of its width. If the length of the diagonal is $\begin{aligned}8\sqrt{10}\end{aligned}$ , then find the perimeter of the rectangle.

60 cm
62 cm
64 cm
66 cm

Answer: Option C

Explanation:

Let Breadth = x cm,
then, Length = 3x cm

$\begin{aligned} x^2+{(3x)}^2 = {(8\sqrt{10})}^2 \\ => 10x^2 = 640 \\ => x = 8 \\ \end{aligned}$
So, length = 24 cm and breadth = 8 cm
Perimeter = 2(l+b)
= 2(24+8) = 64 cm

2. 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

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 farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

10 m * 5 m
15 m * 5 m
20 m * 5 m
25 m * 5 m

Answer: Option C

Explanation:

From the question, 2b+l = 30
=> l = 30-2b

5. 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

Question Detail

A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

1. The length of a rectangle is three times of its width. If the length of the diagonal is $\begin{aligned}8\sqrt{10}\end{aligned}$ , then find the perimeter of the rectangle.

2. 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.

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

4. A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

5. 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 ?

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Question Detail

A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

1. The length of a rectangle is three times of its width. If the length of the diagonal is 8√10\begin{aligned}8\sqrt{10}\end{aligned}, then find the perimeter of the rectangle.

2. 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.

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

4. A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.

5. 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 ?

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1. The length of a rectangle is three times of its width. If the length of the diagonal is $\begin{aligned}8\sqrt{10}\end{aligned}$ , then find the perimeter of the rectangle.

2. 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.