The length of a rectangle is 3 less than twice the width. The perimeter is at least 210 cm. Find the smallest dimension of the r
ectangle.
2 answers:
Answer:
w >= 36
L >= 69
See the image below...
Step-by-step explanation:
L = 2w - 3
P >= 210 cm
P = 2L + 2w, then
2L + 2w >= 210
Since L = 2w - 3, we have
2(2w - 3) + 2w >= 210
Solving left side of the inequality,
4w - 6 + 2w >= 210
6w - 6 >= 210
Adding + 6 in both sides,
6w - 6 + 6 >= 210 + 6
6w >= 216
we isolate w, dividing by 6 both sides,
6w / 6 >= 216 / 6
<h2>w >= 36</h2>L >= 2w - 3
L >= 2(36) - 3
L >= 72 - 3
<h2>L >= 69</h2>Demonstrating,
P >= 2L + 2w
P >= 2(69) + 2(36)
P >= 138 + 72
P >= 210
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