# Answer to Question #1399 in Abstract Algebra 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 + 4x

The area of the outer path is S2-S1 = 4800 + 280x + 4x

Solve the following equation:

4x

x

D = 35

x

x

Answer: the width is 5m.

Let's denote the width as x, thus the area of the whole part whould be

S2 = (80 + 2x)(60+ 2x) = 4800 + 280x + 4x

^{2}The area of the outer path is S2-S1 = 4800 + 280x + 4x

^{2}- 4800 = 4x^{2}+ 280x = 1500Solve the following equation:

4x

^{2}+ 280x -1500 = 0x

^{2}+ 70x - 375 = 0D = 35

^{2}+ 375 = 1600x

_{1}= -35 + 40 = 5x

_{2}= -35 -40 = -75 - out of sence in our case.Answer: the width is 5m.

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