Question

If x = 9 cm and z = 15 cm, what is the length of y?

Answer 1

Given that the problem does not specify if y is opposite, adjacent or hypotenuse side, I will provide two solutions to this problem.

Case 1. Y is the hypotenuse side. (See figure 1)

According to the Pythagorean Theorem, for a right triangle, it is true that:


`c^(2)=a^(2)+b^(2)`

being c the hypotenuse side and a and b the opposite and adjacent side respectively. So, for the figure 1 it is true that:

z = a = 15cm
x = b = 9cm
y = c = ?


`y^(2)=9^(2)+15^(2)=306`
∴
`y=√(306)=17.492cm`

Case 2. Y is the opposite side (The same happens as if it were the adjacent side). (See figure 2)

From the equation:


`c^(2)=a^(2)+b^(2)`

For the figure:

y = a = ?
x = b = 9cm
z = c = 15cm

We need to isolate a, so:


`a^(2)=c^(2)-b^(2)`


`a^(2)=15^(2)-9^(2)=144`

∴
`y=a=√(144)=12cm`