Question

Tomas found the area of a rectangle to be 1/6 square inch. Which could be the side lenghts of the rectangle? A. 1/4 and 2/3 B. 1/3 and 1/3 C. 1/6 and 1/6 D. 1/2 and 1/12

Answer 1

A. 1/4 and 2/3

Step-by-step explanation:

The area of a rectangle is 16 in². Considering a rectangle has 2 side lengths (s₁ and s₂), we can find the area (A) of a rectangle like A = s₁ × s₂

A. 1/4 and 2/3

1/4 × 2/3 = 2/12 = 1/6 These could be the sides of the rectangle because the areas coincide.

B. 1/3 and 1/3

1/3 × 1/3 = 1/9 ≠ 1/6 These could not be the sides of the rectangle because the areas do not coincide.

C. 1/6 and 1/6

1/6 × 1/6 = 1/36 ≠ 1/6 These could not be the sides of the rectangle because the areas do not coincide.

D. 1/2 and 1/12

1/2 × 1/12 = 1/24 ≠ 1/6 These could not be the sides of the rectangle because the areas do not coincide.

Answer 2

A. 1/4 and 2/3

Step-by-step explanation:

The area of a rectangle is the product of its side lengths. The product of (1/4) and (2/3) is ...

`(1)/(4)\cdot(2)/(3)=(1\cdot 2)/(4\cdot 3)=(2)/(12)\\\\=(1)/(6)\qquad\text{the desired area}`