Question

What are two different ways you could find the value of a? Explain these methods.

Answer 1

Sample Response: You could use the Pythagorean theorem, since you know the length of the hypotenuse is 9 + 16 = 25 units and the length of one leg is 15 units. To find the value of a, use the relationship that the the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. You could also use the geometric mean (leg) theorem, which states that the length of the hypotenuse is to the length of an adjacent leg as that adjacent leg length is to the length of its corresponding segment in the hypotenuse. So you could write and solve the proportion 25/a = a/6.

Explanation:

Answer 2

see the attached figure to better understand the problem

we know that

1) First way to find the value of a
in the triangle ABC
applying the Pythagorean theorem
AC²=AB²+BC²--------> BC²=AC²-AB²-----> BC²=25²-15²-----> BC²=625-225
BC²=400--------> BC=20 units
a=BC
a=20 units

2) Second way to find the value of a

in the triangle ABD

AB²=AD²+BD²--------> BD²=AB²-AD²-----> BD²=15²-9²---> BD²=144
BD=12 units

in the triangle BDC
a=BC
BC²=BD²+DC²-----> 12²+16²----> 144+256------> BC²=400
BC=20 units
a=20 units