Chapter 4.9, Problem 8P

To determine

To calculate:Find the new dimensions of the lot.

Answer to Problem 8P

The dimensions of new lot are 22 m and 20 m

Explanation of Solution

Given information: A corner lot that originally was square lost $185m^2$ of the area when one of the adjacent streets was widened by 3 m and the other was widened by 5 m.

Calculation: Let $x$ be the length of the original square plot, Hence the width of new lot is $x-3$ and length of new lot is $x-5$ .

Hence Area of the new lot is $\left(x-5\right)\left(x-3\right)$

Area decreased by 185 square meters, so

Original Area - New Area = 185

  $x^2-\left(x-5\right)\left(x-3\right)=185$

  $x^2-\left(x^2-5x-3x+15\right)=185$

  $8x-15=185$

  $8x=200$

  $x=\frac{200}{8}=25$

So, side of original square is 25 m.

Dimensions of new lot are $\left(x-3\right)=\left(25-3\right)=22$ m and $\left(x-5\right)=\left(25-5\right)=20$

Conclusion: The dimensions of new lot are 22 m and 20 m.