Mathematics
Word Problems and Applications
Practice questions
A square field has a side length of (x) metres. If the side is increased by 8 metres, the area increases by 1216 square metres. What is the value of (x)?The side length of a square is \(x\) cm. If the side length is reduced by 5 cm, the area of the resulting square becomes 784 square cm. What was the original side length of the square?When both length and breadth of a rectangle are increased by (6) cm, the area increases by (480) square cm. If the original length is (12) cm more than the breadth, what is the breadth?The length of a rectangle is 9 m more than its breadth. If the length is increased by 4 m and the breadth by 3 m, the new area becomes 1190 square metres. What is the original breadth of the rectangle?A wire is bent into a square and the area is (1296) square cm. What is the length of the wire?A wire is bent into a rectangle. The length is (16) cm more than the breadth and area is (1344) square cm. What is the length of the wire?A uniform path 3 metres wide surrounds a rectangular garden. The garden is 34 metres long and 22 metres wide. What is the total area including the path?A rectangular garden is 42 m long and 28 m wide. A path of uniform width x m is constructed outside it on all four sides. The total area of the garden and the path is 1848 square metres. What is the value of x?A square field has an outer side of 52 m. After leaving a uniform strip of equal width on all four sides, the inner square has a side of 36 m. What is the width \(x\) of the strip?The sum of squares of two consecutive positive integers is (1201). What is the smaller integer?The sum of the squares of two consecutive positive odd integers is 2050. What is the smaller integer?The sum of squares of two consecutive even positive numbers is (2452). What is the larger number?The difference between two positive numbers is (17) and their product is (1260). What is the larger number?The sum of two positive numbers is 80, and the sum of their squares is 3232. Find the smaller number.A rectangle has length (21) m more than its breadth and area (1870) square m. What is the breadth?The length of a rectangle is 16 cm more than its breadth, and its area is 2145 square cm. What is its length?A rectangle has length (7) m more than its breadth and diagonal (97) m. What is the breadth?A rectangle has area (2494) square cm and length (15) cm more than breadth. What is its perimeter?A rectangular field has perimeter (186) m and area (2016) square m. What is the shorter side?A square park has the same area as a rectangle. The side of the square is 48 m, while the rectangle has breadth \(x\) m and length \((x+28)\) m. What is the value of \(x\)?