Answer:
D
Step-by-step explanation:
The diagram is composed of one large right triangle and inside it it's divided into 2 small right triangles. Since these triangles all have the same shape but not the same size, they are similar triangles. Using similar triangles, create a proportion of side lengths. A proportion is an equation with equal ratios from the large triangle to a small. Notice the large triangle has a hypotenuse of 6+7 = 13 and a leg of x. The small triangle has a hypotenuse of x and a leg of 7.
[tex]\frac{hypotenuse}{leg}=\frac{hypotenuse}{leg}[/tex]
[tex]\frac{13}{x}=\frac{x}{7}[/tex]
To solve for x, cross multiply the numerator with the denominator.
[tex]x*x = 13*7\\x^2 = 91\\x=\sqrt{91} \\x=9.5[/tex]
