Question

Fill in the green box

Answer 1

z = 3√13

Explanation:

y /4 = 9/y

y^2 = 36

y = 6

z^2 = 6^2 + 9^2

z^2 = 36 + 81

z^2 = 117

z = √117

z = √(9 * 13)

z = 3√13

Answer 2

The length of side z is 3√13

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