10.4 Solve applications modeled by quadratic equations  (Page 5/7)

The product of two consecutive odd numbers is 255. Find the numbers.

The product of two consecutive even numbers is 360. Find the numbers.

The product of two consecutive even numbers is 624. Find the numbers.

The product of two consecutive odd numbers is 1023. Find the numbers.

The product of two consecutive odd numbers is 483. Find the numbers.

The product of two consecutive even numbers is 528. Find the numbers.

A triangle with area 45 square inches has a height that is two less than four times the width. Find the height and width of the triangle.

The width of a triangle is six more than twice the height. The area of the triangle is 88 square yards. Find the height and width of the triangle.

The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is three feet. Find the lengths of the three sides of the triangle.

The hypotenuse of a right triangle is 10 cm long. One of the triangle’s legs is three times the length of the other leg. Round to the nearest tenth. Find the lengths of the three sides of the triangle.

A farmer plans to fence off sections of a rectangular corral. The diagonal distance from one corner of the corral to the opposite corner is five yards longer than the width of the corral. The length of the corral is three times the width. Find the length of the diagonal of the corral.

Nautical flags are used to represent letters of the alphabet. The flag for the letter O consists of a yellow right triangle and a red right triangle which are sewn together along their hypotenuse to form a square. The adjoining side of the two triangles is three inches longer than a side of the flag. Find the length of the side of the flag.

The length of a rectangular driveway is five feet more than three times the width. The area is 350 square feet. Find the length and width of the driveway.

A rectangular lawn has area 140 square yards. Its width that is six less than twice the length. What are the length and width of the lawn?

A firework rocket is shot upward at a rate of 640 ft/sec. Use the projectile formula $h=\mathrm{-16}{t}^2+v_{0}t$ to determine when the height of the firework rocket will be 1200 feet.

An arrow is shot vertically upward at a rate of 220 feet per second. Use the projectile formula $h=\mathrm{-16}{t}^2+v_{0}t$ to determine when height of the arrow will be 400 feet.

A bullet is fired straight up from a BB gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula $h=\mathrm{-16}{t}^2+v_{0}t+8$ to determine how many seconds it will take for the bullet to hit the ground. (That is, when will $h=0$ ?)

A city planner wants to build a bridge across a lake in a park. To find the length of the bridge, he makes a right triangle with one leg and the hypotenuse on land and the bridge as the other leg. The length of the hypotenuse is 340 feet and the leg is 160 feet. Find the length of the bridge.

Make up a problem involving the product of two consecutive odd integers. Start by choosing two consecutive odd integers. ⓐ What are your integers? ⓑ What is the product of your integers? ⓒ Solve the equation $n\left(n+2\right)=p$ , where $p$ is the product you found in part (b). ⓓ Did you get the numbers you started with?

Make up a problem involving the product of two consecutive even integers. Start by choosing two consecutive even integers. ⓐ What are your integers? ⓑ What is the product of your integers? ⓒ Solve the equation $n\left(n+2\right)=p$ , where $p$ is the product you found in part (b). ⓓ Did you get the numbers you started with?