Question

can each expression be used to find the area of the rectangle? select yes or no. each □ represents 1 square unit. 3×(10 + 2) 〇 yes 〇 no (3×10)+(3×2) 〇 yes 〇 no 3×(10×2) 〇 yes 〇 no

Explanation:

Step1: Recall area formula

The area of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. The length of the large rectangle is $10 + 2$ and the width is 3. So the area is $A=3\times(10 + 2)$.

Step2: Apply distributive property

By the distributive property $a\times(b + c)=a\times b+a\times c$. Here $a = 3$, $b = 10$ and $c = 2$, so $3\times(10 + 2)=(3\times10)+(3\times2)$.

Step3: Analyze wrong - expression

The expression $3\times(10\times2)$ is incorrect because $10\times2$ does not represent the length of the rectangle. The length is the sum of 10 and 2, not their product.

Answer:

$3\times(10 + 2)$: Yes
$(3\times10)+(3\times2)$: Yes
$3\times(10\times2)$: No