Question

1. a rectangular pen has had its length broken into a 3 - yard section and an 8 - yard section. its width is 5 yards as shown. which of the following calculations would not give the total area of the pen in square yards? (1) 5·3 + 5·8 (2) 5·(3 + 8) (3) 3·5 + 3·8 (4) 15 + 40

Explanation:

Step1: Recall area formula for rectangle

The area of a rectangle is $A = l\times w$. The pen has two - part lengths with a common width of 5 yards. The total area of the pen is the sum of the areas of the two sub - rectangles. The areas of the two sub - rectangles are $5\times3$ and $5\times8$ respectively, and the total area $A=5\times3 + 5\times8$.

Step2: Analyze each option

(1) $5\times3+5\times8$ is the correct way to calculate the area by finding the sum of the areas of the two sub - rectangles.
(2) $5\times(3 + 8)$ uses the distributive property $a\times(b + c)=a\times b+a\times c$, and it is also correct as it first sums the lengths ($3 + 8$) and then multiplies by the width 5.
(3) $3\times5+3\times8$ is incorrect. It does not correctly represent the area of the pen with width 5. The correct terms should have 5 as one of the factors for each part of the area calculation.
(4) $15 + 40$ is correct since $5\times3=15$ and $5\times8 = 40$, and then we sum them to get the total area.

Answer:

(3)