Asked by Yakyra Shelton on Apr 26, 2024
Verified
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 × 16.2716.2716.27 inches
E) 83.583.583.5 inches × 89.589.589.5 inches
Picture
A visual representation of an object, scene, or person produced on a surface.
Dimensions
Measurements that define the size or shape of an object, often used in geometry to describe figures in two or three-dimensional space.
- Address challenges related to the geometrical implications of quadratic functions, such as determining area and perimeter.
Verified Answer
AM
angus mckayApr 29, 2024
Final Answer :
C
Explanation :
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.
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.
Learning Objectives
- Address challenges related to the geometrical implications of quadratic functions, such as determining area and perimeter.