Question

The area of a rectangle is (81x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Answer 1

Answer:

The dimension of the rectangle are $9\cdot x - 2\cdot y$ units and $9\cdot x + 2\cdot y$ units, respectively.

Step-by-step explanation:

Geometrically speaking, the area of a rectangle is equal to the product of its base and its height. If we know that area of the figure is $81\cdot x^{2} - 4\cdot y^{2}$ square units, then we proceed to factor the expression:

1) $A = 81\cdot x^{2} - 4\cdot y^{2}$ Given

2) $A = (9\cdot x -2\cdot y)\cdot (9\cdot x + 2\cdot y)$ $a^{2} - b^{2} = (a + b) \cdot (a - b)$/Result

The dimension of the rectangle are $9\cdot x - 2\cdot y$ units and $9\cdot x + 2\cdot y$ units, respectively.