Question

A fenced in rectangular region with the dimensions 4 yards by 8 yards is suddenly expanded by the same distance in each dimension the resulting region is now 60 square yards in size how much distance was added to each dimension

Answer 1

The distance added to each dimension is 2 yards.

Explanation:

The initial dimensions of the rectangular fence is 8 yards by 4 yards.

The initial area of the rectangular fence = area of a rectangle

area of a rectangle = length x width

So that,

The initial area of the fence = 8 x 4

= 32

The initial area of the fence is 32 square yards.

But, with the new dimensions, area = 60 square yards.

(4 + x) x (8 + x) = 60

`x^(2)` + 12x + 28 = 60

`x^(2)` + 12x - 32 = 0

(x + 14) = 0 or (x - 2) = 0

x = -14 or x =2

Thus, x = 2

The distance added to each dimension is 2 yards.