Question

jacquelyn is creating two - design rectangles for her friends jewelry boxes. for the first design, she can make the width of the box (2x + 5). for the second design, the width must be three times the width of the first design and the length must be 4 more than the width of the first design. the total area of two rectangles can be represented by the expressions ((x)(2x + 5)) and ((3x)(x + 4)). a) what is the area of jacquelyns first design? b) what is the area of jacquelyns second design? c) create an expression that represents the collective area of both designs. select all that apply.

Explanation:

Step1: Find area of first design

We are given the area of first - design as $(x)(2x + 5)$. Using the distributive property $a(b + c)=ab+ac$, we have $x\times2x+x\times5 = 2x^{2}+5x$.

Step2: Find area of second design

The area of the second - design is given by $(3x)(x + 4)$. Using the distributive property, we get $3x\times x+3x\times4=3x^{2}+12x$.

Step3: Find collective area

To find the collective area of both designs, we add the areas of the two designs. $(2x^{2}+5x)+(3x^{2}+12x)$. Combine like - terms: $(2x^{2}+3x^{2})+(5x + 12x)=5x^{2}+17x$.

Answer:

A. The area of the first design is $2x^{2}+5x$.
B. The area of the second design is $3x^{2}+12x$.
C. The collective area of both designs is $5x^{2}+17x$.