Mathematics
Word Problems and Applications
Practice questions
The sum of the squares of two consecutive odd positive integers is 1570. What is the smaller integer?The sum of squares of two consecutive even positive numbers is (1924). What is the larger number?The difference between two positive numbers is (13) and their product is (558). What is the larger number?The sum of two positive numbers is (65) and the sum of their squares is (2125). What is the smaller number?A rectangle has length (14) m more than its breadth and area (1152) square m. What is the breadth?The length of a rectangle is 18 cm more than its breadth, and its area is 1240 square cm. What is the length of the rectangle?A rectangle has length (10) m more than its breadth and diagonal (74) m. What is the breadth?A rectangle has an area of 888 square cm, and its length is 13 cm more than its breadth. What is the perimeter of the rectangle?A rectangular field has perimeter (154) m and area (1480) square m. What is the shorter side?A square park has the same area as a rectangular park. The side of the square is 42 m, while the rectangle has breadth \(x\) m and length \((x+20)\) m. What is the exact value of the rectangle’s breadth \(x\)?The side of a square is \(x+6\) cm and its area is \(1225\ \text{cm}^2\). If the side length is positive, what is the value of \(x\)?The side of a square tile is \(x-8\) cm, and its area is 900 square cm. What is the value of \(x\)?The legs of a right triangle are (x) cm and (x+18) cm and the hypotenuse is (90) cm. What is the smaller leg?The hypotenuse of a right triangle is 109 cm. One leg is 19 cm longer than the other leg. What is the length of the shorter leg?A ladder reaches (60) m up a wall. Its foot is (x) m away from the wall and the ladder length is (x+15) m. What is (x)?A ladder reaches (72) m up a wall. The ladder length is (18) m more than the distance of its foot from the wall. What is that distance?A car covers a distance of 750 km. If its speed is \(x\) km per hour and its travel time is \((x-65)\) hours, what is the speed of the car?A bus covers (560) km. Its speed is (x) km per hour and time is (x-63) hours. What is the time?A boat goes (90) km downstream. Its speed in still water is (x) km per hour and stream speed is (3) km per hour. If time is (5) hours, what is (x)?A person travels 640 km at a speed of \(x+12\) km/h in \(x\) hours. What is the travel time \(x\)?