Concept explainers
Multi Step The height of a painting is twice its width x. You want a 3 inch wide wooden frame for the painting. The area of the frame alone is 216 square inches.
a. Draw a diagram that represents this situation.
b. Write a variable expression for the area of the frame alone.
c. What are the dimensions of the frame?
i.
To graph: The height of a painting is twice of its width
Explanation of Solution
Given:
The height of a painting is twice of its width
Calculation:
It is given that width of the painting is
ii.
To calculate: The height of a painting is twice of its width
Answer to Problem 41P
The expression for the area of frame alone is
Explanation of Solution
Given:
To find the area of frame alone we should subtract the area of smaller rectangle from the area of larger rectangle from the figure shown in above part.
Calculation:
Let
Conclusion:
The expression for the area of frame alone is
iii.
To calculate: The height of a painting is twice of its width
Answer to Problem 41P
The length of frame is 28 inches and the width of frame is 14 inches
Explanation of Solution
Given:
The area of the frame alone is 216 square inches
Calculation:
From the above part we know the expression of the area of frame alone is
Now we know the expression for the area of frame alone and its area also so by equating them we get
Width of frame is 14 inches and its length is twice of width, so
length
Conclusion:
The length of frame is 28 inches and the width of frame is 14 inches.
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