Question

question 1 - 13
the length of 2 adjacent sides of a rectangle are represented by (z + 5) feet and (3z + 4) feet. in terms of z, what is the area, in square feet, of the rectangle?
(4z + 9) ft²
(19z + 19) ft²
(3z²+20) ft²
(3z² + 9z + 20) ft²
(3z² + 19z + 20) ft²

Explanation:

Step1: Recall area formula for rectangle

The area $A$ of a rectangle is given by $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=(z + 5)$ and $w=(3z + 4)$.

Step2: Multiply the two binomials

Use the FOIL method: $(z + 5)(3z+4)=z\times3z+z\times4 + 5\times3z+5\times4$.

Step3: Simplify the expression

$z\times3z+z\times4 + 5\times3z+5\times4=3z^{2}+4z + 15z+20=3z^{2}+19z + 20$.

Answer:

$(3z^{2}+19z + 20)\text{ ft}^2$