Question

I am the fencing around the rectangular lion exhibit at a zoo . The lions have 1,000 square meters to roam inside a rectangular area that is 15 meters longer than it is wide. If I were to unwind and make myself straight , how long would I be?

Answer 1

Area (A) = Length (L) x Width (w)
1000 = (w + 15)(w)
1000 = w² + 15w
0 = w² + 15 - 1000
Use Pythagorean Theorem to solve for w:
w =
`\frac{-b +/- \sqrt{b^(2) - 4ac}}{2a} = \frac{-15 +/- \sqrt{15^(2) - 4(1)(-1000)}}{2(1)} = (-15 +/- √(225 + 4000))/(2)`
= (-15 +/- 65)/2 =
`(-15 + 65)/(2), (-15 - 65)/(2) = (50)/(2), (-80)/(2) = 25, -40`

Since the width cannot be negative, w = -40 is not valid.
w = 25
L = w + 15 → L = (25) + 15 → L = 40

The question is asking for the perimeter:
Perimeter (P) = 2·L + 2·w
= 2(40) + 2(25)
= 80 + 50
= 130

Answer: If you unwind the fence, it would be 130 ft long