## Area Problems Solved Questions For IBPS, SBI and Other Bank Exams - Page 3

**Question 1**

Find the area of the rectangle whose perimeter is 212 units and length exceeds breadth by 28 units.

a) 3967 b) 2613 c) 5213 d) 1945

**Answer : **b) 2613

Solution:

Let the breadth of the rectangle be X.

Then its length = X + 28

We know that the perimeter of the rectangle = 2(l + b)

2(X + 28 + X) = 212

2X + 28 = 106

2X = 78

X = 39

i.e., Breadth X = 39 units

Length = X + 28 = 39+28 = 67

Area of the rectangle = length x breadth = 39 x 67 = 2613 sq.units.

Hence the required answer is 2613.

**Question 2**

What will be the breadth of the rectangle if the area is 781.25 sq.units and length is 25 % more than the breadth ?

a)39 b)23 c)52 d)25

**Answer :** d)25

Solution :

Let the breadth be X units.

length = X + 25X/100 = 125X/100 units

Area = 781.25 sq.units

Area = length x breadth

i.e.,(125X/100)(X) = 781.25

125X^{2} / 100 = 781.25

125X^{2} = 78125

X^{2} = 78125/125

X^{2} = 625

X = 25

**Question 3**

What is the breadth of the rectangle if the length is 18 units and the area and perimeter of the rectangle are in the ration 18 : 5 ?

a)12 b)26 c)36 d)52

**Answer : **a)12

Solution :

Area of the rectangle = lb

Perimeter = 2(l+b)

Given lb / 2(l+b) = 18/5

And l = 18

Then ratio = 18b / 2(18 + b) = 18/5

b/2(18+b) = 1/5

5b = 2(18+b)

3b = 36

b = 12 units.

Hence the breadth of the rectangle is 12.

**Question 4**

The difference between the perimeter of the rectangle and one of its side is 30 units. The area of the rectangle is 100 sq.units. Find the length and breadth.

a)10,10 b)25,4 c)50,2 d)none of these

**Answer :** a)10,10

Solution :

Let L and B be the length and breadth of the rectangle.

Perimeter = 2(l + b)

Given that, difference between the perimeter of the rectangle and its one side is 30 units

Without loss of generality assume that side as b.

Then 2(L + B) - B = 30

2L + B = 30

B = 30 - 2l

Area = LB = 100 sq.untis,

Then L(30 - 2L) = 100

30L - 2L^{2} - 100 = 0

2L^{2} + 30L + 100 = 0

L^{2} + 15L + 50 = 0

(L-10)(L-5) = 0

L = 10 or L = 5

If L = 10 then B = 30 - 2l = 10

If L = 5 then B = 30 - 2l = 20

Therefore the answer is either 10,10 or 20,5

From the given options, the answer is 10,10