ANSWER
x = 16
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:
[tex]\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}[/tex]
Using Similar triangles, we have that:
[tex]\begin{gathered} \frac{7}{y}\text{ = }\frac{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}[/tex]
That is the value of x.
