Question

A wooden board measuring 12 inches by 8 inches (in.) is to be shortened uniformly along all sides as shown. By what length should each side be shortened if the revised wooden board is to have an area of 45 square inches?A. 1.5B. 2.1C. 3.19D. 4.25

Answer 1

Formulating an equation to represent this situation, we have:

w*l= A (w=width, l=length, A= Area)

(8-x)(12-x) = 45 (Replacing and subtracting x on each side)

96 - 8x -12x + x^2 =45 (Multiplying the expressions)

x^2 - 8x -12x +96 - 45 = 0 (Subtracting 45 on both sides of the equation and organizing)

x^2 - 20x + 51 = 0 (Adding like terms)

(x - 17)(x-3) = 0 (Factoring)

Separating into two equations:

x- 17 = 0 --> x= 17

x - 3= 0 --> x = 3

We can see that the viable solution is 3 as both sides are less than 17. So, the answer would be 1.5 as we have to shorten 1.5 on one side and 1.5 on the other. The answer is option A.