SOLUTION: A photograph that measures 20 cm by 35 cm is to be surrounded by a matte before framing. The
width of the matte will be equal on all four sides. If the area of the matte will be t
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width of the matte will be equal on all four sides. If the area of the matte will be t
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Question 160902: A photograph that measures 20 cm by 35 cm is to be surrounded by a matte before framing. The
width of the matte will be equal on all four sides. If the area of the matte will be twice the area of
the photograph, determine the width of the matte. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A photograph that measures 20 cm by 35 cm is to be surrounded by a matte before
framing. The width of the matte will be equal on all four sides.
If the area of the matte will be twice the area of the photograph, determine
the width of the matte.
:
Let x = width of the matte
:
20 * 35 = 700 sq cm is the area of the photo
then
2(700) = 1400 sq cm is the area of the matte
:
The dimension of the matte will be (2x+20) by (2x+35)
:
I am assuming that the matte will not be behind the photo, just around it
Therefore we can find the area using these dimensions, assuming the area will
be 2100 sq cm with 700 sq cm (which is behind the photo) not counted
giving us a matte area of 1400 sq cm
:
(2x + 20) * (2x + 35) = 2100
FOIL
4x^2 + 70x + 40x + 700 = 2100
:
4x^2 + 110x + 700 - 2100 = 0
:
4x^2 + 110x - 1400 = 0
Simplify divide by 2
2x^2 + 55x - 700 = 0
This equation requires the quadratic formula:
In this equation; a=2; b=55; c=-700
:
:
Solve this and you should get a positive solution: x = 9.4677 cm as the width
;
A rough check using a calc: 2x = 19
(20+19*)(35+19) = 2106 cm - 700 (behind the photo) = 1406 sq/cm area of the matte
