Mathematics
Word Problems and Applications
Practice questions
The sum of squares of two consecutive positive integers is (1513). What is the smaller integer?The sum of the squares of two consecutive positive odd numbers is 2314. What is the smaller number?The sum of squares of two consecutive even positive numbers is (3044). What is the larger number?The difference between two positive numbers is (19) and their product is (1632). What is the larger number?The sum of two positive numbers is 90, and the sum of their squares is 4068. Find the smaller number.A rectangle has length (23) m more than its breadth and area (2220) square m. What is the breadth?The length of a rectangle is 19 cm more than its breadth, and its area is 2772 square cm. What is the length of the rectangle?A rectangle has length (15) m more than its breadth and diagonal (75) m. What is the breadth?The area of a rectangle is 2170 square centimetres, and its length is 27 centimetres more than its breadth. What is the perimeter of the rectangle?A rectangular field has perimeter (202) m and area (2508) square m. What is the shorter side?A square park has the same area as a rectangle. The side of the square is 56 m, while the rectangle has breadth \(x\) m and length \((x+66)\) m. What is the value of the rectangle’s breadth \(x\)?The side of a square is (x+17) cm, and its area is (3249) square cm. Find the value of (x).The side of a square tile is \(x-12\) cm and its area is 1849 square cm. What is the value of \(x\)?The legs of a right triangle are (x) cm and (x+30) cm and the hypotenuse is (150) cm. What is the smaller leg?The hypotenuse of a right triangle is 185 cm, and one leg is 37 cm longer than the other leg. What is the length of the shorter leg?A ladder reaches (120) m up a wall. Its foot is (x) m away from the wall and the ladder length is (x+50) m. What is (x)?A ladder reaches (84) m up a wall. The ladder length is (42) m more than the distance of its foot from the wall. What is that distance?A car covers a distance of 800 km. If its speed is \(x\) km/h and its travel time is \((x-92)\) hours, what is the speed of the car?A bus covers a distance of 1056 km. If its speed is \(x\) km/h and its travel time is \((x-85)\) hours, how much time does it take to complete the journey?A boat goes (216) km downstream. Its speed in still water is (x) km per hour and stream speed is (5) km per hour. If time is (8) hours, what is (x)?