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The length of the rectangle is 2 less than 3 times as long as the width. If the perimeter is 76 cm, find the dimensions of the rectangle.

Sagot :

Charlespangueidn

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.

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