PERIMETERS
A perimeter is the measure of the distance AROUND an object.
l
S
S
S
w
w
S
l
Perimeter of a Rectangle
=w+l+w+l
= 2w + 2l
Perimeter of a Square
= S +S+ S + S
= 4S
Triangles
Scalene Triangle
l2
l1
Isosceles Triangle
(2 sides and 2 angles are equal)
C
l3
Perimeter of a Scalene Triangle
= l1 + l2 + l3
Equilateral Triangle
(3 sides and 3 angles are equal)
s
C
A
s
B
s
s = AC = BC =AB
A =
B =
C
Perimeter of an Equilateral Triangle
=s+s+s
= 3s
s
s
B
A
t
S=AC=BC
A =
Perimeter of an
Isoceles Triangle
=s+s+t
= 2s + t
B
Example:
The perimeter of a rectangle is 26 ft. The length of the rectangle is 1 ft more than twice
the width. Find the width and length of the rectangle.
Step 1) What are we trying to find? The width and length of the rectangle.
Let w = width, and l = length.
Given info: Perimeter is 26 ft. It is a rectangle, so the formula for a rectangle’s perimeter
is P = 2w + 2l.
Also, length of the rectangle is 1 ft more than twice the width.
Step 2) Make an equation from given info.
Perimeter = 26 ft = 2w + 2l
Length is 1 ft more than twice its width.
l
= 1
+
2w
We can combine these equations to solve for each variable, w and l.
26 = 2w + 2l
Substitute equation, l = 1 + 2w for l in the above equation.
26 = 2w + 2(1 + 2w)
Step 3) Solve equation
Use distributive property to get rid of parentheses.
26 = 2w + 2 + 4w
Combine like terms
26 = 6w + 2
24 = 6w
4=w
What about l? l = 1 + 2w = 1 + 2(4) = 1+8=9
Step 4) Check result. Perimeter with w=4 and l=9 should be 26
26 = 2(4) + 2(9)= 8 + 18 = 26 Yes.
Step 5) State conclusion (Remember the measuring units!)
The width of the rectangle is 4 ft and the length is 9 ft.
Example 1 The perimeter of an isosceles triangle is 25 ft.
The length of the third side is 2 ft less than the length of one of
the equal sides. Find the measures of the three sides of the
triangle.
Now you try this one:
A carpenter is designing a square patio with a perimeter of 52 ft.
What is the length of each side?