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Alex777 [14]
3 years ago
8

The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft? What is the length of the

field?
80 ft
100 ft
120 ft
140 ft
Mathematics
2 answers:
Scilla [17]3 years ago
6 0

Answer:

The answer is 120 feet.

Step-by-step explanation:

The area of the field (A) is:

A = w · l       (w - width, l - length)

It is known:

A = 12,000 ft²

l = w - 20

So, let's replace this in the formula for the area of the field:

12,000 = w · (w - 20)

12,000 = w² - 20

⇒ w² - 20w - 12,000 = 0

This is quadratic equation. Based on the quadratic formula:

ax² + bx + c = 0      ⇒  

In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000

Thus:

So, width w can be either

or

Since, the width cannot be a negative number, the width of the field is 120 feet.

lutik1710 [3]3 years ago
6 0

Answer:

L = 120 ft

Step-by-step explanation:

W = L-20

W x L = 12000

(L-20) x L = 12000

L^2 -20L -12000 = 0

(L + 100)(L - 120 ) = 0

L = 120 ft

W = 100 ft

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