A zookeeper is buying fencing to enclose a pen at the zoo. The pen is an isosceles right triangle. There is already a fence alon

Question

4 years ago

8

A zookeeper is buying fencing to enclose a pen at the zoo. The pen is an isosceles right triangle. There is already a fence alon

g the hypotenuse, which borders a path. The area of the pen will be 4,500 square feet. The zookeeper can buy the fencing in whole feet only. How many feet of fencing should he buy?

Mathematics

1 answer:

pav-90 [236] · Answer 1 · 2022-01-11T18:31:33+03:00

Answer:

He should buy 189.47 feets.

Step-by-step explanation:

Since there's a hypotenuse this triangle is rectangular and since it's an isosceles triangle we know that both cathetus are equal. We were given the area of this triangle, wich is 4500 square feet, the equation to compute this area is A = b*h/2, since the cathetus are equal b = h and we can solve for either of this variables. So we have:

A = b*b/2

4500 = b*b/2

b*b= 9000

b = sqrt(9000) = 94.87 feet

Since the hypotenuse of this triangle already has a fence we only need to buy the fencing for the cathetus, wich should be two times b, since there are two cathetus. So the amount of fence is 2*b = 2*94.87 = 189.74 feets.