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Math 100
Word Problems (geometric figures)
Use the figure and the information below it to write an equation involving x.
Find the lengths of all sides.
1. The length of a rectangle is twice its width. If the perimeter is 60, find the
dimensions of the rectangle.
2. The side of a triangle have lengths 7, x, and x+1. If the perimeter is 30, find the
value of x.
3. A triangle has two equal sides and a third side that is 15 cm long. If the perimeter
is 50 cm, how long is each of the two equal sides.
4 - 9 find the value of x.
4.
5.
52
6.
3xo
o
(x + 5)o
xo
xo
43o
7.
10o
xo
23o
8.
2xo
(2x – 2)o
9.
xo
(3x - 17)o
xo
xo
(x + 40)o
Set 1 Answers
35
2
3.
x=
6.
9.
x = 29
x = 27
1.
4.
w = 10 and l = 20
x = 85
2.
5.
x = 11
x = 30
7.
x = 147
8.
x = 60
(2x - 5)o
Rectangle and Triangle Problems
Solve the following problems on a separate sheet of paper
Use the four step process
1. Define variables
2. Set up an equation
3. Solve the equation
4. Answer the question
1. Find the sides of a rectangle if the length is 3 less than the width. The perimeter of
the rectangle is 54 inches.
2. Find the sides of a rectangle if the length is 9 more than the width. The perimeter is
58cm.
3. Find the sides of a rectangle if the length is 2 more than three times the width and the
perimeter of the rectangle is 52 inches.
4. Find the sides of a rectangle if the length is twice the width and the perimeter of the
rectangle is 72 feet.
5. Find the sides of a rectangle if the length is 12 less than three times the width and the
perimeter of the rectangle is 56 feet.
6. Find the 3 sides of a triangle if the second side is 10 more than the first side and the
third side is 4 less than 2 time s the first side. The perimeter of the triangle is 38 cm.
7. Find the 3 sides of a triangle if the second side is 10 more than the first side and the
third side is 25 less than 2 times the first side. The perimeter of the triangle is 65mm.
8. Find the 3 sides of a triangle if the second side is 2 more than two times the first side
and the third side is 2 less than three times the first side. The perimeter of the triangle
is 42 yards.
9. Find the 3 sides of triangle if the second side is 10 more that first side and third side is
5 more than the second side. The perimeter if the triangle is 70 feet.
10. Find the 3 angles of a triangle if the second angle is 30 less than the first and the third
angle is 3 times the first angle.
11. Find the 3 angles of a triangle if the second angle is 20 more than the first angle and
the third angle is 50 less than the first angle.
12. Find the 3 angle of a triangle if the second angel is 40 more than the first angle and
the third angle is twice the first angle.
13. Find the 3 angles of a triangle if the second angle is 10 more than twice the first angle
and the third angle is 60 more than the second angle.
Answers
1. 15, 12
3. 6, 20
5. 10, 18
7. 20, 30, 15
9. 15, 25, 30
11. 20, 70, 90
13. 20, 50, 110
2. 10, 19
4. 12, 24
6. 8, 12, 18
8. 7, 16, 19
10. 12, 42, 126
12. 35, 70, 75