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The rectangle shown has a perimeter of 148 cm and the given area. Its length is 8 more than five times its width. Write and solve a system of equations to find the dimensions of the rectangle.​

User Muteshi
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1 Answer

17 votes
17 votes

Answer:

System of equations:

L = 5W + 7

2W + 2L = P

L = 62 cm

W = 11 cm

Explanation:

Given the measurements and key words/phrases in the problem, we can set up two different equations that can be used to find both variables, length and width, of the rectangle.

The formula for perimeter of a rectangle is: 2W + 2L = P, where W = width and L = length. We also know that the L is '7 more than five times its width'. This can be written as: L = 5W + 7. Using this expression for the value of 'L', we can use the formula for perimeter and solve for width:

2W + 2(5W + 7) = 146

Distribute: 2W + 10W + 14 = 146

Combine like terms: 12W + 14 = 146

Subtract 14 from both sides: 12W + 14 - 14 = 146 - 14 or 12W = 132

Divide 12 by both sides: 12W/12 = 132/12 or W = 11

Put '11' in for W in the equation for 'L': L = 5(11) + 7 or L = 55 + 7 = 62.

User Mortb
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