Quadratic Area Word Problems #2

By Jeanmarie Mullen
Last updated over 3 years ago
15 Questions
1.

The area of a square is 21 more than its perimeter. Find the length of the side of the square. [Only an algebraic solution will be accepted.]

[Type your answers in this form: 4 and 9 ]

2.

The length of a rectangle is 1 more than the side of a square and the width of the rectangle is 1 less than the side of the square. If the area of the rectangle is 35, find the length of the side of the square. [Only an algebraic solution will be accepted.]

[Type your answers in this form: 4 and 9 ]

3.

Two squares have sides p cm and (p + 5) cm. The sum of their squares is 625 sq cm. Find the sides of the squares. [Only an algebraic solution will be accepted.]

[Type your answers in this form: 4 and 9 ]

4.

A rectangular picture measures 6 inches by 8 inches. Simon wants to build a wooden frame for the picture so that the framed picture takes up a maximum area of 100 square inches on his wall. The pieces of wood that he uses to build the frame all have the same width. Write an equation or inequality that could be used to determine the maximum width of the pieces of wood for the frame Simon could create.

Solve the equation or inequality to determine the maximum width of the pieces of wood used for the frame to the nearest tenth of an inch. [Only an algebraic solution will be accepted.]

[Type your answers in this form: 4 and 9 ]

5.

A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an area of 396 square meters.

Write an equation that can be used to find x, the width of the walkway.

Determine and state the width of the walkway, in meters. [Only an algebraic solution will be accepted.]

[Type your answers in this form: 4 and 9 ]

6.

New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters.

The new rectangular garden will have an area that is 25% more than the original square garden. Write an equation that could be used to determine the length of a side of the original square garden.

Determine the area, in square meters, of the new rectangular garden. [Only an algebraic solution will be accepted.]

[Type your answers in this form: 4 and 9 ]

7.

A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters.

Determine, algebraically, the dimensions of the garden in meters. [Only an algebraic solution will be accepted.]

[Type your answers in this form: 4 and 9 ]

8.

The length of a photograph is 1 cm less than twice the width.
The area is 45 cm2 . Find the dimensions of the photograph.

[Type your answers in this form: 4 and 9 ]

9.

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10.

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11.

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12.

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13.

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14.

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15.

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