Problema Solution
If you are making a picture frame of uniform width for a square picture that has side lengths of 2 feet. The total area of the frame is 5 square feet. What is the length of the sides of the frame?
Answer provided by our tutors
let
w = the width of the frame, w>0
a = 2 ft is the length of the sides of the square picture
a + 2w = 2 + 2w is the length of the sides of the frame
the total area of the frame = total area - the are of the picture
the total area of the frame is 5 square feet:
5 = (a + 2w)^2 - a^2
(a + 2w)^2 - a^2 = 5
(2 + 2w)^2 - 2^2 = 5
by solving we find:
w = 0.5 ft
click here to see the step by step solution of the equation:
2 + 2*0.5 = 3 ft
the length of the sides of the frame is 3 ft.