A picture is 6 inches longer than it is wide and has an area of 167 square inches. What are the dimensions (in inches)of the picture. Round your answers to two decimal places.
A) 12.92 inches × 18.92 inches
B) 4.27 inches × 10.27 inches
C) 10.27 inches × 16.27 inches
D) 4.27 inches × $16.27$ inches
E) $83.5$ inches × $89.5$ inches

Question

A picture is 6 inches longer than it is wide and has an area of 167 square inches. What are the dimensions (in inches)of the picture. Round your answers to two decimal places.
A) 12.92 inches  × 18.92 inches
B) 4.27 inches  × 10.27 inches
C) 10.27 inches  × 16.27 inches
D) 4.27 inches  × $16.27$ inches
E) $83.5$ inches  × $89.5$ inches

Quizplus · Accepted Answer

Let's set up an equation to solve for the dimensions of the picture. Let x be the width:

Length = x + 6
Area = Length x Width = (x + 6) x x = x^2 + 6x

We know that the area is 167 square inches, so we can set up an equation:

x^2 + 6x = 167

Rearranging, we get:

x^2 + 6x - 167 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

With a = 1, b = 6, and c = -167, we get:

x = (-6 ± sqrt(6^2 - 4(1)(-167))) / 2(1)
x = (-6 ± sqrt(1244)) / 2
x = (-6 ± 35.24) / 2

We can ignore the negative root, so:

x = (-6 + 35.24) / 2 = 14.62

Therefore, the width of the picture is 14.62 inches and the length is x + 6 = 20.62 inches.

Rounded to two decimal places, the answer is Choice C: 10.27 inches x 16.27 inches.

A Picture Is 6 Inches Longer Than It Is Wide 16.2716.2716.27

A Picture Is 6 Inches Longer Than It Is Wide $16.27$