29. A photograph is 16 inches wide and 9 inches long and is surrounded by a frame of uniform
width. If the area of the frame is 84 square inches, find the uniform width of the frame.
A. 15 in.
B. 16 in.
C. 17 in.
D. 18 in.
width. If the area of the frame is 84 square inches, find the uniform width of the frame.
A. 15 in.
B. 16 in.
C. 17 in.
D. 18 in.
Answers & Comments
Answer:
Step-by-step explanation:
w = 16 in
l = 9 in
x = the uniform width of the frame, x>0 (the width can not be negative number)
A1 = 84 in^2 area of the frame
A = the area of photograph and frame
the width of the photograph and frame is: 16 + 2x
the length of the photograph and frame is: 9 + 2x
A = (16 + 2x)(9 + 2x)
the area of the photograph is = A - A1
A - A1 = l*w
(16 + 2x)(9 + 2x) - 84 = 16*9
simplifying we get the quadratic equation:
2x^2 - 25x - 42 = 0
by solving we find:
x = 1.5 in