Mathematics
Word Problems and Applications
Practice questions
The sum of squares of two consecutive positive integers is (365). What is the smaller integer?The sum of the squares of two consecutive positive odd numbers is 650. What is the smaller number?The sum of squares of two consecutive even positive numbers is (1060). What is the larger number?The difference between two positive numbers is (5) and their product is (456). What is the larger number?The sum of two positive numbers is (55) and the sum of their squares is (1525). What is the smaller number?A rectangle has length (8) m more than its breadth and area (1056) square m. What is the breadth?The length of a rectangle is 12 cm more than its breadth, and its area is 864 square cm. What is the length of the rectangle?A rectangle has length (7) m more than its breadth and diagonal (65) m. What is the breadth?The area of a rectangle is 720 square cm, and its length is 6 cm more than its breadth. What is the perimeter of the rectangle?A rectangular field has perimeter (118) m and area (840) square m. What is the shorter side?A square park has the same area as a rectangular park. The side of the square is 30 m, while the breadth of the rectangle is (x) m and its length is (x+15) m. What is the positive value of the rectangle’s breadth (x)?The side of a square is \((x+4)\) cm, and its area is \(576\) square cm. What is the value of \(x\)?The side of a square tile is \((x-3)\) cm and its area is \(441\) cm². If the side length is positive, what is the value of \(x\)?The legs of a right triangle are (x) cm and (x+14) cm and the hypotenuse is (70) cm. What is the smaller leg?The hypotenuse of a right-angled triangle is \(85\) cm. One leg is \(13\) cm longer than the other leg. What is the length of the smaller leg?A ladder reaches (40) m up a wall. Its foot is (x) m away from the wall and the ladder length is (x+10) m. What is (x)?A ladder reaches (24) 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 240 km. If its speed is \(x\) km/h and the travel time is \((x-46)\) hours, what is the speed of the car?A bus covers a distance of 360 km. Its speed is \(x\) km/h and its travel time is \((x-54)\) hours. What is the travel time?A boat goes (48) km downstream. Its speed in still water is (x) km per hour and stream speed is (4) km per hour. If time is (4) hours, what is (x)?