A portrait has dimensions of 50 inches by 60 inches and is surrounded by a frame of uniform width. If the total area (portrait p
lus frame) is 3456 square inches, find the width of the frame
1 answer:
Answer:
2 inches
Step-by-step explanation:
If x is the width of the frame, then the overall dimensions are ...
(50 +2x) by (60 +2x)
so the area is ...
3456 = (50 +2x)(60+2x)
x^2 +55x -114 = 0 . . . . . . . divide by 4, subtract the left side
(x +57)(x -2) = 0 . . . . . . . . . factor
Solutions to this are x=2 and x=57 (extraneous).
The width of the frame is 2 inches.
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Answer: second option
Step-by-step explanation:
The standard form of a quadratic equation is:
Then, to write the quadratic equation given in the problem in standard form, you must substract 1 from both sides of the equation. Then you have:
Given the quadratic equation above, to find the value of you must substitute:
a=2; b=5 and c=-1 into
Thenrefore, you obtain the following result: