Question

statement a: area of a rectangle with measured length = 2.536 m and width = 1.4 m. statement b: area of a rectangle with measured length = 2.536 m and width = 1.41 m. since you are not told specific numbers of significant figures to round to, you must use the rules for multiplying numbers while respecting significant figures. if you need a reminder, consult the hint. determine the correct relationship between the statements. view available hint(s) statement a is greater than statement b. statement a is less than statement b. statement a is equal to statement b.

Explanation:

Step1: Calculate area of rectangle in Statement A

The formula for the area of a rectangle is $A = l\times w$. Given $l = 2.536$ m and $w = 1.41$ m. So $A_A=2.536\times1.41 = 3.57576$ m². When considering significant - figures, the number with the least number of significant figures in the multiplication is 1.41 (3 significant figures). So, $A_A\approx3.58$ m².

Step2: Calculate area of rectangle in Statement B

Given $l = 2.536$ m and $w = 1.4$ m. Using the area formula $A = l\times w$, we have $A_B=2.536\times1.4 = 3.5504$ m². Since 1.4 has 2 significant figures, $A_B\approx3.6$ m².

Step3: Compare the two areas

Since $3.58<3.6$, Statement A is less than Statement B.

Answer:

Statement A is less than Statement B.