Question

Originally the dimensions of a rectangle were 15cm by 20cm. When both dimensions were decreased by the same amount, the area of the rectangle is half the area of the original rectangle. Find the dimensions of the new rectangle.

Answer 1

Explanation:

We can write an equation to represent this problem.

(15 + w)(20 + w) = 1/2 (15)(20)

Foil out the left side of the equation.

300 + 35w + w^2 = 150

Subtract 150 from both sides.

w^2 + 35w + 150 (I rearranged it to be in the form that is most efficient)

Now solve for variable w using the quadratic equation (look up the formula if necessary)

[-35 +_ (square root of the value of 1225-600)] / 2

[-35 +_ (SqRt of 625)] /2

(-35 +_ 25) /2

= -30, -5

I just realized that it can't increase by a negative number, so I'm not really sure of the answer. Sorry, my bad. However, I feel that this may be of help to other people anyway, so I think I'll leave it up here. Apologies again.

Feel free to read through my reasoning behind my answer, and see if it gives you any ideas or inspiration for solving this problem.