SOLUTION: A 10cm by 17cm picture is mounted with a border of uniform width on a rectangular frame. If the total area of the border is 198cm^2, find the dimension of the frame.

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Question 883838: A 10cm by 17cm picture is mounted with a border of uniform width on a rectangular frame. If the total area of the border is 198cm^2, find the dimension of the frame.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Border Plus Picture equals 198 square centimeters.

Border? Unknown.

Picture: 10%2A17 square centimeters.

Border plus Picture: Let x = the uniform width of border.
%2810%2B2x%29%2817%2B2x%29=198.

Solving for x will allow finding the outside dimensions and the inside dimensions for the frame.

170%2B34x%2B20x%2B4x%5E2=198
34x%2B20x%2B4x%5E2=28
54x%2B4x%5E2=28
2x%5E2%2B27x=14
2x%5E2%2B27x-14=0

x=%28-27%2B-+sqrt%2827%5E2-4%2A2%2A%28-14%29%29%29%2F%282%2A2%29
x=%28-27%2B-+sqrt%28841%29%29%2F%282%2A2%29
x=%28-27%2B-+29%29%2F4, MUST USE PLUS FORM.
-
highlight%28x=1%2F2+%2Acm%29

Outside dimensions of the frame, 10.5 cm and 17.5 cm

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A 10cm by 17cm picture is mounted with a border of uniform width on a rectangular frame. If the total area of the border is 198cm^2, find the dimension of the frame.


Dimensions of frame: highlight_green%28highlight_green%2816_by_23%29%29 cm



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