mike wants to fence in part of his backyard. he wants the length of the fenced - in area to be at least 20…

mike wants to fence in part of his backyard. he wants the length of the fenced - in area to be at least 20 feet long, $lgeq20$. he has 200 feet of fencing. the inequality that models the possible perimeter of the yard is $2l + 2wleq200$. which are possible dimensions for mikes backyard? check all that apply. $w = 50$ ft; $l = 10$ ft $w = 10$ ft; $l = 50$ ft $w = 20$ ft; $l = 60$ ft $w = 90$ ft; $l = 30$ ft $w = 50$ ft; $l = 40$ ft

mike wants to fence in part of his backyard. he wants the length of the fenced - in area to be at least 20 feet long, $lgeq20$. he has 200 feet of fencing. the inequality that models the possible perimeter of the yard is $2l + 2wleq200$. which are possible dimensions for mikes backyard? check all that apply. $w = 50$ ft; $l = 10$ ft $w = 10$ ft; $l = 50$ ft $w = 20$ ft; $l = 60$ ft $w = 90$ ft; $l = 30$ ft $w = 50$ ft; $l = 40$ ft

Answer

Answer:

B. $w = 10$ ft; $l = 50$ ft C. $w = 20$ ft; $l = 60$ ft E. $w = 50$ ft; $l = 40$ ft

Explanation:

Step1: Recall the perimeter - inequality

We have the inequality $2l + 2w\leq200$ and the condition $l\geq20$.

Step2: Check option A

For $w = 50$ ft and $l = 10$ ft, $l=10<20$, does not satisfy $l\geq20$.

Step3: Check option B

For $w = 10$ ft and $l = 50$ ft, $2l+2w=2\times50 + 2\times10=100 + 20=120\leq200$ and $l = 50\geq20$.

Step4: Check option C

For $w = 20$ ft and $l = 60$ ft, $2l+2w=2\times60+2\times20 = 120 + 40=160\leq200$ and $l = 60\geq20$.

Step5: Check option D

For $w = 90$ ft and $l = 30$ ft, $2l+2w=2\times30+2\times90=60 + 180 = 240>200$, does not satisfy $2l + 2w\leq200$.

Step6: Check option E

For $w = 50$ ft and $l = 40$ ft, $2l+2w=2\times40+2\times50=80 + 100=180\leq200$ and $l = 40\geq20$.