Answer:
The length of side z is 3√13
Step-by-step explanation:
From the attachment above, there are 3 triangles all which are right angled.
To solve for z, we need to get the value of either x or y or both.
The simplest way is to solve for y;
Using comparison of similar triangles;
We can compare sides of triangles to give;
9/y = y/4 ---- solve for y
y² = 4 * 9
y² = 36 ---- Fund square root of both sides
y = √36
y = 6
Now that we've solved for y;
Using Pythagoras theorem, we can get the value of z
Consider the 3 sides of the triangle where z is the hypothenus!
z² = y² + 9²
Substitute 6 for y
z² = 6² + 9²
z² = 36 + 81
z² = 117 ---- Take Squareroot of both sides
z = √117
z = √(9 * 13)
z = √9 * √13
z = 3 * √13
z = 3√13
Hence, the length of side z is 3√13
