The width of a rectangle is 17 inches less than $\frac { 1 } { 2 }$ of its length. If the perimeter of the rectangle 98 inches, find the area of the rectangle. ( Hint: Find the width and the length first. )
A) $550 \mathrm { in } ^ { 2 }$
B) $5 \mathrm { in } ^ { 2 }$
C) $44 \mathrm { in } ^ { 2 }$
D) $220 \mathrm { in } ^ { 2 }$
E) $110 \mathrm { in } ^ { 2 }$

Question

The width of a rectangle is 17 inches less than $\frac { 1 } { 2 }$  of its length. If the perimeter of the rectangle 98 inches, find the area of the rectangle. ( Hint: Find the width and the length first. )
A) $550 \mathrm { in } ^ { 2 }$
B) $5 \mathrm { in } ^ { 2 }$
C) $44 \mathrm { in } ^ { 2 }$
D) $220 \mathrm { in } ^ { 2 }$
E) $110 \mathrm { in } ^ { 2 }$

Quizplus · Accepted Answer

Let the length be $ l $. Then the width is $ \frac{l}{2} - 17 $. The perimeter is given by $ 2l + 2(\frac{l}{2} - 17) = 98 $. Solving this equation gives $ l = 44 $ and width $ = 5 $. The area is $ 44 \times 5 = 220 \mathrm{in}^2 $.

The Width of a Rectangle Is 17 Inches Less Than 12\frac { 1 } { 2 }21​

The Width of a Rectangle Is 17 Inches Less Than $\frac { 1 } { 2 }$