Question

question: 10 the models below represent the shape of two sections of carpet. each section is made up of squares and rectangles and the dimensions shown are in feet. section 1 section 2 how much greater is the area, in square feet, of section 1 than section 2? a. $x^{2}+5x + 25$ b. $x^{2}+25$ c. $x^{2}+15x$ d. $x^{2}-5x + 25$

Explanation:

Step1: Calculate area of Section 1

Section 1 has three rectangles with dimensions \(x\times x\) and one rectangle with dimensions \(5\times(x + 5)\). The area of the three \(x\times x\) rectangles is \(3x^{2}\), and the area of the \(5\times(x + 5)\) rectangle is \(5(x + 5)=5x+25\). So the total area of Section 1, \(A_1=3x^{2}+5x + 25\).

Step2: Calculate area of Section 2

Section 2 has three rectangles with dimensions \(x\times x\) and one rectangle with dimensions \(5\times x\). The area of the three \(x\times x\) rectangles is \(2x^{2}\), and the area of the \(5\times x\) rectangle is \(5x\). So the total area of Section 2, \(A_2 = 2x^{2}+5x\).

Step3: Find the difference in areas

Subtract the area of Section 2 from the area of Section 1: \(A_1 - A_2=(3x^{2}+5x + 25)-(2x^{2}+5x)=3x^{2}+5x + 25 - 2x^{2}-5x=x^{2}+25\).

Answer:

B. \(x^{2}+25\)