Question

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 rectangle.

Answer 1

check the picture below

Answer 2

w >= 36

L >= 69

See the image below...

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

w >= 36

L >= 2w - 3

L >= 2(36) - 3

L >= 72 - 3

L >= 69

Demonstrating,

P >= 2L + 2w

P >= 2(69) + 2(36)

P >= 138 + 72

P >= 210