Learn about Applications of Quadratic Equations using Square Roots Word problems, quadratic equations. So the problem it states, a zookeeper is buying fencing to enclose a pen at the zoo. The pen is an isosceles right triangle. There is already a fence on the side that borders a path. The area of the pen would be is 4,500 square feet. The zookeeper can buy the fencing in the whole feet. How many feet of fencing should he buy? So since the hypotenuse is already fenced, so this is the hypotenuse of our triangle. It’s already fenced. We need fencing for the other two equal sides of the triangular pen. So we’re going to let L represent the length of one side. So that means the zookeeper needs L+L fencing, feet of fencing because we already have this side of fencing. So we need L+L fencing. So here are the steps that we need to find L. So now we need to find L. We don’t know what L is. We need to find it. So the first thing we need to do is we need to write a formula to help us solve this problem. So an area of a triangle, so when you're looking for the area of a triangle, it’s the ½×B×H. All right, so now we have our formula. So the second thing we need to do is we’re going to substitute L for both the base and the height. So we’re going to substitute the L for the base and the height. And the area, we know is 4,500. So we’re going to go ahead and make our substitutions. So the area is 4,500=½ times the base L and times our height which is L. So now, we’re going to simplify. So we’re going to multiply both sides by 2 and I'm going to multiply this side by 2 and so 4,500 that would give me a 9,000 and this would give me the ½. So the two and the two cancel out, so it would be L×L. So then 9,000=L2. So I'm just going to rewrite this, so it’s L2=9,000. It doesn’t matter either way; I just rewrote it this way to help me out a little bit. So now, what I'm going to do is take the square root of both the sides, so I'm going to use the positive and negative to show both square roots. So I'm going to take the square roots, so L=v9,000 and -v9,000. So the best estimate of the v9,000 because 9,000 is not a perfect square. So the best estimate would be 94.8, so 94.8 is about 95. So that means that L would be 95 or -95. So the lengths are not negative because you can't have a negative length. So the length is not negative, so that means that the length is about 95 feet. So 95 is the only possible solution because you can't have a negative length. So that means that the zookeeper needs, if we go back and we said that the length of our sides, the zookeeper will need L+L feet. So the zookeeper would need 95+95 which is 190 feet of fencing. So keep in mind that remember, if you have x2=A and A is a positive real number then x=va and the -va. And remember that we can use the square root of perfect squares to help estimate the square roots of other numbers. Remember that if A is not a perfect square and A is between two perfect squares that are close to A. So for example, 40 is between, so if I had the v40 that is not a perfect square. But 40 is between 36 and 49.