Question

The perimeter of a rectangle with length l and width w is 44 inches. The area of the rectangle is at most 120. Which of the following statements is true?

A. If w 12 inches, then l >_ 10 inches
B. If w 12 inches, then l > 10 inches
C. If w 12 inches, then l <_ 10 inches
D. If w 12 inches, then l < 10 inches

Answer 1

oh OK 
Perimeter = 2l + 2w = 44
l + w = 22
if l = 12 then w = 120/12 = 10
if l <_ 12 then w >_ 10

Its A 

Answer 2

If w ≤ 12 , l≥10 , Option A is the correct answer.

What is In Equality ?

Inequality is a mathematical phrase that uses terms like larger than, less than, is not equal to, and so on, and solving it is analogous to solving equations.

Any integer that, when entered into an equation or inequality, will fulfill the equation or inequality is referred to as the solution.

It is given that the perimeter of a rectangle with length l and width w is 44 inches.

Perimeter of a rectangle = 2(l+b) = 2(l+w)

44 = 2(l+w)

l+w = 22

Area of the rectangle = 120

l * b = 120

l * w = 120

l = 120/w

120/w  + w = 22

120+ w² = 22w

w²-22w +120 = 0

w² -12w-10w +120 = 0

w(w-12) -10(w-12)

(w-12)(w-10) = 0

w=12 , l=10

w=10, l =12

If w ≤ 12 , l≥10 , therefore Option A is the correct answer.

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