Question

multiple choice 1 point the sides of a rectangle have a length of 6x - 4 units and a width of 7x + 9 units long. which of the following represents the area of the rectangle? 42x² + 26x - 36 42x² + 82x - 36 13x² - 18x - 36 56x² - 54x + 36

Explanation:

Step1: Recall area formula for rectangle

Area = length × width

Step2: Substitute given expressions

$\text{Area} = (6x - 4)(7x + 9)$

Step3: Apply FOIL method

First terms: $6x \times 7x = 42x^2$
Outer terms: $6x \times 9 = 54x$
Inner terms: $-4 \times 7x = -28x$
Last terms: $-4 \times 9 = -36$

Step4: Combine like terms

$42x^2 + 54x - 28x - 36 = 42x^2 + 26x - 36$

Answer:

$42x^2 + 26x - 36$ (Option A)