Word Problems on Algebraic Inequalities based on Mensuration

Q.

A soccer field is $100m$ long and $75m$ wide. What is the perimeter of the field ?

Q.

Sonu runs around a square park of side $80m$ five times. What distance does he cover? Ankit runs thrice around a rectangular park of length $250m$ and breadth $150m$. What distance does he cover? Who covers more distance and by how much?

Q.

Monika went to a park which is $600m$long and $300m$wide. She took three complete rounds around its boundary. What distance did she cover ?

Q.

The length and breadth of a rectangular field are in the ratio $6:5$. If the perimeter of the field is $2200$ m, then the length of the field is

1. $550m$

2. $600m$

3. $650m$

4. $1100m$

Q. A bus can hold a maximum of 35 passengers. There are 5 seats reserved for older people, 15 seats for general people. If the remaining seats are for women, then what's the maximum number of seats reserved for women?

1. 5
2. 10
3. 15
4. 25

Q.

The ratio of length to the width of a sheet of paper is $4:3$ . If the length is $16cm$, find the width?

Q. A rectangular room has a length of $x$ m and breadth of ($x+2$) m and the perimeter of the room is less than 24 m. Calculate the maximum length of the room if $x$ is a positive integer.

1. 4 m
2. 6 m
3. 8 m
4. 2 m

Q. Jaffar has a square canvas with sides of 60cm length. He wants to turn it into a rectangle by reducing one pair of opposite sides, but he does not want to decrease the area by more than 10%. By how much can he reduce the length of one pair of opposite sides of the square?

1. Reduction ≤ 6 cm
2. Reduction < 9 cm
3. Reduction ≤ 7 cm
4. Reduction < 8 cm

Q.

A farmer has a rectangular field of length and breadth $240m$ and $180m$ respectively. He wants to fence it with $3$ rounds of rope. What is the total length of rope he must use?

Q.

The length and the breadth of three rectangles are as follows:

(a) $9\text{m}$ and $6\text{m}$

(b) $17\text{m}$ and $3\text{m}$

(c) $4\text{m}$ and $14\text{m}$

Which one has the largest area and which one has the smallest?

Q. John has a profit of $\$150$ in the month of October. The profit was at least $\$12$ more than the previous month. Determine the maximum profit he made in the month of September.

1. $\$135$
2. $\$138$
3. $\$136$
4. $\$137$

Q. The length of a rectangle is 4 more than two times the width. The minimum perimeter is 80. Determine the minimum length of the rectangle that can satisfy the condition.

1. 28
2. 12
3. 30
4. 32