The perimeter of a rectangle is 180 180 180 inches. The length of the rectangle is four ext { four } four times its width. Find the area of the rectangle.A) 5 , 184 5,184 5 , 184 square inchesB) 2 , 592 2,592 2 , 592 square inchesC) 5 , 508 5,508 5 , 508 square inchesD) 1 , 296 1,296 1 , 296 square inchesE) 720 720 720 square inches

Question

The perimeter of a rectangle is   180 180 180   inches. The length of the rectangle is    four  	ext { four }  four    times its width. Find the area of the rectangle.A)    5 , 184 5,184 5 , 184   square inchesB)    2 , 592 2,592 2 , 592   square inchesC)    5 , 508 5,508 5 , 508   square inchesD)    1 , 296 1,296 1 , 296   square inchesE)    720 720 720   square inches

Chantelle Mzizi · Accepted Answer

Final Answer : D, Explanation :   The perimeter of a rectangle is given by   2 ( l + w ) 2(l + w) 2 ( l + w )  , where   l l l   is the length and   w w w   is the width. Given   l = 4 w l = 4w l = 4 w   and the perimeter is   180 180 180   inches, we can write   2 ( 4 w + w ) = 180 2(4w + w) = 180 2 ( 4 w + w ) = 180  , simplifying to   10 w = 180 10w = 180 10 w = 180  , thus   w = 18 w = 18 w = 18   inches. The length   l = 4 w = 72 l = 4w = 72 l = 4 w = 72   inches. The area of the rectangle is   l × w = 72 × 18 = 1 , 296 l 	imes w = 72 	imes 18 = 1,296 l × w = 72 × 18 = 1 , 296   square inches.

The perimeter of a rectangle is $180$ inches. The length of the rectangle is $\text { four }$ times its width. Find the area of the rectangle.

A) $5, 184$ square inches
B) $2, 592$ square inches
C) $5, 508$ square inches
D) $1, 296$ square inches
E) $720$ square inches

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