Answer:
Dimensions of the rectangle whose perimeter is 76 are;
Length = 28 cm
Width = 10 cm
Step-by-step explanation:
Step 1: Write the formula for the perimeter of the rectangle.
P = 2 ( L + W )
Step 2: Create an Algebraic Equation based on the formula or substitute all of the values given in the problem.
Given:
P = 76
L = 2 less than 3 times as long as the width (3W-2)
Formula:
P = 2 ( L + W )
76 = 2 [ ( 3W - 2 ) + W ]
Step 3: Simplify the equation.
76 = 2 ( 3W + W - 2 )
76 = 2 ( 4W - 2 )
76 = 8W - 4
76 + 4 = 8W
80 = 8W
[tex]\frac{80}{8}[/tex] = [tex]\frac{8W}{8}[/tex]
10 cm = Width
Step 4: Substitue the value of W in the equation of the length in order to find its value.
Length = 3W - 2
Length = 3 (10) - 2
Length = 30 - 2
Length = 28 cm
Conclusion: Therefore the value of the dimensions (length and width) of a rectangle with a perimeter of 76 cm are, 28 cm and 10 cm respectively.
