Answer to Question #1399 in Abstract Algebra for mohsin

Question

The lenth of inner rectangle is 80m,and its breadth is 60m,find the width if the area of the outer path is 1500msq

Answer 1

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.