The area of a rectangle is 180 and the perimeter is 54. What are the dimensions?

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Answer 1 · 2018-04-19T02:36:11

#color(maroon)("Length " = 15, " Width " = 12#

#"Area of Rectangle "= A = L * W = 180#

#L = 180 / W#

#"Perimeter of Rectangle " = P = 2W + 2L = 54#

Substituting the value of L in terms of W;

#2W + (2 * 180) / W = 54#

#2W^2 - 54W + 360 = 0#

#2W^2 + 24W + 30W + 360 = 0#

#2W ( W + 12) + 30 *(W + 12) = 0#

#(2W + 30) * (W + 12) = 0#

#W = -15, -12#

#W = 12, 15, " as length cannot be negative"#

#L = 180 / W = 15, 12#

Since length is greater than the width, measurements are

#color(maroon)("Length " = 15, " Width " = 12#