Question

Two square rooms have a total floor area of 89m2. One room is 3m longer each way than the other. Find the dimensions of the two rooms. A. 5m square and 8m square B. 4m square and 6m square C. 5m square and 12m square D. 6m square and 8m square

Answer 1

A

Explanation:

Let the smaller room have an area of x^2

Let the larger room have an area of (x + 3)^2

(x+3) ^2 + x^2 = 89 Be careful not to make it 89^2.

x^2 + 6x + 9 + x^2 = 89 Expand the binomial squared

2x^2 + 6x + 9 - 89 = 0 Subtract 89 from both sides

2x^2 + 6x + 9 - 89 = 0 Combine

2x^2 + 6x - 90=0 Divide by 2

x^2 + 3x - 45 = 0 This factors.

(x + 9)(x- 5) = 0

X + 9 gives nothing useful

x - 5 = 0

x = 5

x + 3 = 5+3 = 8

So the answer is A