Question

Find the missing length indicated. Leave your answer in simplest radical form.Please do problems 15 and 16

Answer 1

x = 16

Step-by-step explanation

15. We are given the triangle.

We need to find x.

We first have to find the base of the largest triangle using Pythagoras.

Let us name the side y:

We have that:

`\begin{gathered} y^2=7^2\text{ + (3}\sqrt[]{7})^2\text{ = 49 + 63} \\ y^2\text{ = 112} \\ y\text{ = }\sqrt[]{112} \\ y\text{ = 4 }\sqrt[]{7} \end{gathered}`

Using Similar triangles, we have that:

`\begin{gathered} (7)/(y)\text{ = }(y)/(x)\text{ } \\ \Rightarrow y^2\text{ = 7 }\cdot\text{ x} \\ x\text{ = }\frac{(4\sqrt[]{7})^2}{7}\text{ = }\frac{16\cdot\text{ 7}}{7} \\ x\text{ = 16} \end{gathered}`

That is the value of x.