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Answer on Abstract Algebra Question for mohsin

Question #1399
The lenth of inner rectangle is 80m,and its breadth is 60m,find the width if the area of the outer path is 1500msq
Expert's answer
The area on the inner part is S1 = 80 * 60 = 4800 m2
Let's denote the width as x, thus the area of the whole part whould be
S2 = (80 + 2x)(60+ 2x) = 4800 + 280x + 4x2
The area of the outer path is S2-S1 = 4800 + 280x + 4x2 - 4800 = 4x2 + 280x = 1500
Solve the following equation:
4x2 + 280x -1500 = 0
x2 + 70x - 375 = 0
D = 352 + 375 = 1600
x1 = -35 + 40 = 5
x2 = -35 -40 = -75 - out of sence in our case.
Answer: the width is 5m.

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