These lessons are compiled to help Algebra 1 students learn how to solve geometry word problems using quadratic equations.

**Related Pages**

Geometry Word Problems

Geometry Word Problems Worksheets

Quadratic Equations

**Example:**

A picture inside a frame is 2 in longer than it is wide. The picture is in a frame that has width 3 in
on each side of the picture. If the area of the picture, including the frame is 195 in^{2},
find the dimensions of the frame.

**Example:**

Suppose a gardener wants to fence two equal rectangular plots. If she has 31 yards of fencing and the
total area of the plots is to be 40 yd^{2}, what are the possible dimensions?

**Example:**

Suppose a gardener wants to fence three rectangular plots. If she has 120 yards of fencing and the
total area of the plot is 450 yard^{2}, give the dimensions of the plots.

**Example:**

Suppose the area of a rectangle is 114.4m^{2} and the length is 14m longer than the width.
Find the length and width of the rectangle.

This problem requires the use of the Pythagorean Theorem to find the lengths of the sides of a piece of property in the shape of a right triangle.

**Example:**

Taylor finds a piece of property in the shape of a right triangle. She finds that the longer leg
is 10 m shorter than twice the length of the shorter leg and the hypotenuse is 20 m longer than
the longer leg. Find the lengths of the sides of the triangular lot.

How to solve three different types of word problems that require one to use quadratic equations?

**Examples:**

- Find the two consecutive positive even numbers whose sum of their square is 580.
- A rectangular building measuring 30 m by 25 m is going to have its area increased by 200 m
^{2}by adding a strip of uniform width to all four sides. Determine the width of the strip. - The hypotenuse of a right angle triangle is 3 cm longer than one of the legs, and 6 cm longer than the other leg. Find the lengths of the three sides of the triangle.

**Examples:**

- One leg of a right triangle is 4 inches longer than the other leg. The hypotenuse is 20 inches long. How long is the shorter of the legs?
- The sides of a right triangle are x, x+1, and x+2 units long. Find the side lengths of the triangle by solving for x.

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