Question

The area of a rectangle is (25x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.

Answer 1

(5x+3y) and (5x-3y)

Explanation:

From the concept on difference between two squares;

a² - b² = (a+b)(a-b)

Therefore;

25x² - 9y² = (5x+3y) (5x-3y)

Therefore the dimensions of the square are (5x+3y) and (5x-3y)

Answer 2

the dimensions of the rectangle are (5x + 3y) and (5x - 3y)

Explanation:

The area of a rectangle is 25x^2 - 9y^2 square units.

To find the dimensions of a rectangle we need to factorize the expression completely.

We know that (a + b)(a - b) = a^2 - b^2

In this case: a^2 = 25x^2 and b^2 = 9y^2

So a = sqrt(25x^2) = 5x

And b = sqrt (9y^2) = 3y

Then the solution is:

(a + b)(a - b) = (5x + 3y)(5x - 3y)

Then the dimensions of the rectangle are (5x + 3y) and (5x - 3y)