Problema Solution
a photograph is 16 inches wide and 9 inches long and is surrounded by a frame of uniform width x. if the area of the frame is 84 square inches, find the uniform width of the frame.
a.what is the area of photograph and frame?
b.given the area of the frame which is 84 sq. inches, formulate the rel. among three areas.
c.what kind of equation form?
how can you solve the value of x?
Answer provided by our tutors
let
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
click here to see the step by step solution of the quadratic equation:
the uniform width of the frame is 1.5 inches.