Area with Explanation

Q1. A farmer wants to fence a 100 sq. m rectangular garden. But he has 30 meters barbed wire; he can fence only three sites of that garden. His house wall serves as a 4th side of the fencing. What is the dimension of the garden?

Answer- Option C

Explanation-

We have : 2b + l = 30
l = 30 - 2b.
Area = 100 m²
l x b = 100
b(30 - 2b) = 100
b² - 15b + 50 = 0
When b = 10, l = 10 and when b = 5, l = 20.
Since the garden is rectangular, so its dimension is 20 m x 5 m.

Q2. Three sites of a rectangular parking space are marked by yellow paint. If the sum of the length of the painted side is 37 feet and length of an unpainted side is 9 feet then find the area of this parking space?

Answer- Option A

Explanation-

Clearly, we have : l = 9 and l + 2b = 37 or b = 14.
Area = (l x b) = (9 x 14) sq. ft. = 126 ft. ft.

Q3. A brick of dimensions 20 cm x 10 cm is to be used for flooring a hall having dimensions 25 m long and 16 m broad. Find the number of bricks required?

Answer- Option B

Explanation-

Number of bricks =

Area of hall Area of 1 brick

2500 x 1600 20 x 10

= 20000.

Q4. The breath of a rectangular playground is 60% of its length. If the perimeter of the ground is 800 m, find the area of this playground?

Answer- Option D

Explanation-

Let length = x meters.
Then, breadth =

60x 100

meters =

3x 5

meters.

Perimeter =

2

x +

3x 5

meters =

16x 5

meters.

16x 5

= 800

meters.

x =

800 * 5 16

= 250 m.

So, length = 250 m; breadth = 150 m.
Area = (250 * 150) m² = 37500 m²

Q5. The perimeter of a rectangular carpet is 46 meters, and its area is 120 sq.m. What is the length of its diagonal?

Answer- Option B

Explanation-

2(l + b) = 46 or l + b = 23, Also, lb = 120.

Diagonal =    l² + b² =   (l + b)² - 2lb

=   (23)² - 240 = 17m.

Q6. The difference between the length and the breadth of a blackboard is 8 cm. If the breadth is decreased by 4 cm and the length is increased by 7 cm, the area remains the same. Find the dimensions of the blackboard?

Answer- Option D

Explanation-

Let breadth = x cm. Then, length = (x + 8) cm.
(x + 8)x = (x + 15)(x - 4)
= x² + 8x = x² + 11x - 60
x = 20.
So, length = 28 cm and breadth = 20 cm.

Q7. The breadth of a rectangular field is increased by (r + 5)%, and the length decreased by r%. If the area of the field is unchanged, what is the value of r?

Answer- Option A

Explanation-

Let original length = x and original breadth = y.
Then, original area = xy.
New area =

(100 - r)x 100

(105 + r)y 100

=

10500 - 5r - r2 10000

xy

10500 - 5r - r2 10000

xy = xy

r² + 5r - 500 = 0
(r + 25)(r - 20) = 0
r = 20.