61.5k views
1 vote
A 5 in by 7in photograph is surrounded by a frame of uniform width the area of the frame equals the area of the photograph find the width of the frame

User Joyann
by
7.5k points

1 Answer

6 votes

Let x be the width of the frame.
Area of the picture is 5*7 = 35 sq in

Area of the frame given as the same, frame = 35 sq in also


Therefore the total area (picture & frame) will be 70 sq in



A simple equation would be made and it will look like this: (7+2x) * (5+2x) = 70

Using the FOIL method
35 + 14x + 10x + 4x^2 = 70
4x^2 + 24x + 35 - 70 = 0; subtract 70 from both sides:
4x^2 + 24x - 35 = 0


unluckily this will not factor easily, so we should use the quadratic equation:
where: a = 4; b = 24; c = -35

x = -b sqrt b^2 – 4*a*c divided by 2 * a

x = -24
± sqrt 24^2 -4*4*(-35) divided by 2*4

x = -24
±sqrt 576 - -(560) divided by 8

x = -24
± sqrt 576 + 560 divided by 8

x = -24
± sqrt1136 divided by 8

x = -24 + 33.7046 divided by 8
x = 9.7046 divided by 8
x =1.213 inches is the answer

User Manjiro Sano
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories