SOLUTION: The outside of a picture frame measures 14 in by 20 in. 148 in squared of the picture shows. Find the thickness of the frame.

Algebra ->  Length-and-distance -> SOLUTION: The outside of a picture frame measures 14 in by 20 in. 148 in squared of the picture shows. Find the thickness of the frame.       Log On


   

Question 1057404: The outside of a picture frame measures 14 in by 20 in. 148 in squared of the picture shows. Find the thickness of the frame.

Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
Let t be the thickness of the frame. Then:
(20-2w)(14-2w)=148
280-68w+4w²-148=0
4w²-68w+132=0
Using the quadratic formula,w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ , we get two roots: 14.7649820431 and 2.23501795693. The most sensible choice is that the frame is 2.23501795693 in. thick. ☺☺☺☺
If 232 sq. in. are showing, then:
(20-2w)(14-2w)=232
280-68w+4w²-232=0
4w²-68w+48=0
w²-17w+12=0
Using the quadratic formula, i.e. x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+, we get two roots: 16.2620873481 and 0.73791265187. The only logical choice is a frame that is 0.73791265187 in. in thickness. ☺☺☺☺