## Area Problems Solved Questions For IBPS, SBI and Other Bank Exams - Page 7

Area Problems Solved Questions (Page 7 of 7)

**Question 1**

The area of rectangular field of length 90 meters and breadth 80 meters is equal to the area of a square plot. What will be the length of the diagonal of the square plot?

a) 120m b) 100m c) 99m d) 105m

**Answer : **a) 120m

Solution :

Given that the length of the rectangular field l = 90 m and breadth = b = 80 m.

Then its area lb = 90 x 80 sq.m

We know that the area of square = (1/2)x(diagonal)^{2}

from the given question, we have area of square plot = area of rectangular field

That is, 90 x 80 = 1/2 x diagonal^{2}

diagonal^2 = 2 x 7200 = 14400 = (120)^{2}

diagonal = 120 m.

**Question 2**

What will be the ratio of the area of a square to that of the rectangle if the breadth of the rectangle and the side of the square are equal and the length of the rectangle is 40% more than its breadth?

a) 4:9 b) 5:6 c) 5:7 d) 3:5

**Answer : **c) 5:7

Solution :

Let the breadth be X m.

Then, length = 40% more than X = 140% of X = 140X/100 = 7X/5

Area of rectangle = lb = (7X/5)X = (7/5)X^{2} sq.m

Given that, breadth of the rectangle = side of the square

Therefore, area of the square = X^{2}

Required ratio = X^{2} : 7(X^{2})/5

= 1:7/5 = 5:7

Hence the answer is option c.

**Question 3**

If the areas of a square and rectangle are the same then which of the following will be true?

a) Perimeter of the square is greater than the perimeter of the rectangle

b) Perimeter of the square is equal to that of the rectangle

c) Perimeter of the square is less than the perimeter of the rectangle

d) Cannot be determined.

**Answer :** c) perimeter of the square is less than the perimeter of the rectangle

Solution :

If the areas of a square and rectangle are same then perimeter of the square is less than the perimeter of the rectangle.

For example, take a square of side 4cm and a rectangle having l = 8cm and b = 2cm.

Now, area of the square = 4x4 = 16 sq.cm

Area of the rectangle = lb = 8x2 = 16 sq.cm

And, the perimeter of the square= 4a = 16 cm

Perimeter of the rectangle = 2(l+b) = 2(10) = 20cm

Hence, option c is true.

**Question 4**

If a square and a rectangle have equal perimeter then which of the following will be true?

a) Area of the square is less than the area of the rectangle

b) Area of the square is equal to that of the rectangle

c) Area of the square is greater than the area of the rectangle

d) Cannot be determined.

**Answer : **c) Area of the square is greater than the area of the rectangle

Solution :

If the square and the rectangle have equal perimeter then the area of the square is greater than that of the rectangle.

For example, take a square of side 6cm and a rectangle having l = 7cm, b = 5cm

Now, the perimeter of the square = 4a = 24cm

And the perimeter of the rectangle = 2(l+b) = 24cm

Area of the square = 16 sq.cm

Area of the rectangle = 7x5 = 35 sq.cm

Hence the option c is true.

Area Problems Solved Questions (Page 7 of 7)