Word Problems

Geometry Word Problems Involving Perimeter

Example 1:

A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?

Solution:

Step 1: Assign variables:

Let x = length of the equal side
Sketch the figure


Step 2: Write out the formula for perimeter of triangle.

P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

50 = x + x + x+ 5

Combine like terms
50 = 3x + 5

Isolate variable x
3x = 50 – 5
3x = 45
x =15

Be careful! The question requires the length of the third side.

The length of third side = 15 + 5 =20

The following video is about writing an equation and finding the dimensions of a rectangle knowing the perimeter and some information about the about the length and width.

Geometry Word Problems Involving Area

Example 1:

A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle?

Solution:

Step 1: Assign variables:

Let x = original width of rectangle
Sketch the figure
Step 2: Write out the formula for area of rectangle.

A = lw

Step 3: Plug in the values from the question and from the sketch.

60 = (4x + 4)(x –1)

Use distributive property to remove brackets
60 = 4x2 – 4x + 4x – 4

Put in Quadratic Form
4x2 – 4 – 60 = 0
4x2 – 64 = 0

This quadratic can be rewritten as a difference of two squares
(2x)2 – (8)2 = 0

Factorize difference of two squares
(2x)2 – (8)2 = 0
(2x – 8)(2x + 8) = 0

We get two values for x.


Since x is a dimension, it would be positive. So, we take x = 4

The question requires the dimensions of the original rectangle.
The width of the original rectangle is 4.
The length is 4 times the width = 4 × 4 = 16