Word Problems - Quadratics

The outside of a picture frame has a length which is 8 cm more than width. The area enclosed by the outside of the picture frame is 65 square cm. Find the width of the outside of the picture frame.

• 5 cm
• 8 cm
• 21 cm
• 13 cm

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

The area of a square is numerically 96 more than the perimeter. Find the length of the side.

• 12 units
• 288 units
• 72 units
• 48 units

The height of a box is 3 inches. The length is three inches more than the width. Find the width if the volume is 390 square inches.

• 3 inches
• 10 inches
• 13 inches
• 130 inches

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

• 3 ft²
• 1 ft²
• 2.2 ft²
• 1.5 ft²

Tags

CCSS.HSA.CED.A.1

Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 9 mi, the distance between the cars was 3 mi more than the distance traveled by the car heading east. How far had the east bound car traveled?

• 18 miles
• 15 miles
• 12 miles
• 9 miles

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18ft. Find the length of the ladder if the length is 6ft more than its distance from the wall.

• 30 ft.
• 36 ft.
• 24 ft.
• 18 ft.

A boat is 92 feet from the base of cliff.  If the distance from the top of the cliff to the boat is 23 less than twice the height of the cliff to the water.  Find the height of the cliff.  Round to the nearest tenth of a foot if necessary.

• 38.3 ft.
• 53.7 ft.
• 69 ft.
• 115 ft.

The position of an object moving in a straight line is given by s = 2t² - 3t, where s is in meters and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 9 meters?

• 2.8 sec.
• 10.0 sec.
• 13.5 sec.
• 3.0 sec.

A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s(t) = 16t² + 32t where s is in feet. How long (to the nearest tenth) will it take the ball to fall 224 feet?

• 2.7 sec.
• 8.4 sec.
• 3.7 sec.
• 2.9 sec.

The difference of the squares of two positive consecutive even integers is 28.  Find the integers.

• 6, 4
• 4, 2
• 6, 8
• 8, 10