Question

question 1 (5 points) a rectangular yard is enclosed by 100 meters of fencing. the table shows some possible values for the length and width of the yard. complete the table with the missing value of a, b, and c.

Explanation:

Step1: Recall rectangle - perimeter and area formulas

The perimeter of a rectangle is $P = 2(l + w)$ and the area is $A=l\times w$. Given that the perimeter $P = 100$ meters, so $l + w=\frac{P}{2}=50$, which means $l = 50 - w$.

Step2: Find the value of 'a'

We know that $A=l\times w$. When $l = 20$ and $w = 30$, then $a=l\times w=20\times30 = 600$ square - meters.

Step3: Find the value of 'b'

Since $l + w = 50$, when $l = 35$, then $b=50 - 35=15$ meters.

Step4: Find the value of 'c'

When $l = 40$ and $w = 10$, then $c=l\times w=40\times10 = 400$ square - meters.

Answer:

a = 600, b = 15, c = 400