A GUIDE TO SOLVING WORD PROBLEMS
1) Read the problem carefully as many times as necessary until you understand the situation.
2) Draw a sketch or diagram, underline any key words, identify any formulas that need to be
used.
3) Choose a letter to represent the quantity you want to find and label accordingly.
4) Write an equation and solve.
5) Check the solution with the information in the original word problem. Did you answer the
question the problem is asking? Does the answer make sense?
PERIMETER WORD PROBLEMS
The perimeter of any figure is the sum of all its sides.
When a word problem gives information about the perimeter of a figure you will know the
equation you should use to help you get the answer.
EXAMPLES:
1) In a triangle, one side is three times as large as the smallest side and the third side is 40 feet
more than the smallest side. The perimeter of the triangle is 184 feet. Find the measurements of
all three sides.
A triangle has three sides. Since the perimeter was given, the equation will be the following:
side one + side two + side three = perimeter
Let first side (smallest) = x
second side = 3x
third side = 40 + x
equation:
solve:
x + (3x) + (40 + x) = 184
5x + 40 = 184
5x = 144
x = 28.8
Since the question asked for the measurement of all three sides, go to the labels and complete the
computation.
first side (smallest) = x = 28.8 ft
second side = 3x = 3(28.8) = 86.4 ft
third side = 40 + x = 40 + 28.8 = 68.8 ft
The measurements of the triangle are 28.8 ft, 86.4 ft, and 68.8 ft.
2) The length of a rectangle is 5 cm less than three times its width. If the perimeter of the
rectangle is 54 cm, find the length and width.
A rectangle has 4 sides in which opposite sides are equal. Therefore, the perimeter
will be the following:
(Length will be represented by L and the width will be represented by W.)
Perimeter = L + L + W + W
or
P = 2L + 2W
Let width = x
length = 3x - 5
equation:
solve:
54 = 2(3x - 5) + 2 (x)
54 = 6x - 10 + 2x
54 = 8x - 10
64 = 8x
8=x
To answer the question go back to the labels and compute.
width = x
= 8 cm
length = 3x - 5 = 3(8) - 5 = 19 cm
The length of the rectangle is 19 cm and the width of the rectangle is 8 cm.
3) The width of a rectangle is twice the length. The perimeter is 104 feet. Find the dimensions.
Let
length = x
width = 2x
equation:
solve:
use P = 2L + 2W
104 = 2(x) + 2(2x)
104 = 2x + 4x
104 = 6x
17 1/3 = x
The dimensions of a rectangle is referring to the length and width.
length = x = 17 1/3 ft
width = 2x = 2(17 1/3) = 34 2/3 ft
The dimensions of the rectangle are 17 1/3 ft by 34 2/3 ft.
4) If one side of a square is increased by 8 cm and an adjacent side decreased by 2 cm, a
rectangle is formed whose perimeter is 40 cm. Find the length and width of the rectangle.
A square has four equal sides. Since we have a square becoming a rectangle, a table will be
constructed to show the relationship.
square
rectangle
length
x
x+8
width
x
x-2
Since the rectangle's perimeter was given and we have the dimensions, we use the formula 2L +
2W = P.
equation:
solve:
40 = 2(x + 8) + 2(x - 2)
40 = 2x + 16 + 2x - 4
40 = 4x + 12
28 = 4x
7=x
The value of x = 7 is the length and width of the square. However, the question is asking for the
rectangle's dimensions.
length = x + 8 = 7 + 8 = 15 cm
width = x - 2 = 7 - 2 = 5 cm
The length of the rectangle is 15 cm and the width of the rectangle is 5 cm.
5) The length of a garden is 10 cm longer than three times the width. The perimeter of the
garden is 240 cm2. Find the area of the garden.
The area of a rectangle is length times width (A = L x W). Therefore, we need to find the length
and width. Since the perimeter was given, we can use that formula to find the length and width,
and then apply the area formula.
Let length = 3x + 10
width = x
equation: 240 = 2(3x + 10) + 2(x)
solve:
240 = 6x + 20 + 2x
240 = 8x + 20
220 = 8x
27.5 = x
length = 3x + 10 = 3(27.5) + 10 = 92.5 cm
width = x
= 27.5 cm
Now use the length and width to find the area; A = 92.5(27.5) = 2543.75 cm2.
The area of the garden is 2543.75 cm2.