Respuesta :

Answer:

x = 3

Step-by-step explanation:

In the figure attached, the two triangles are shown.

Given that both triangles are similar, then its sides are proportional. That allows us to write the following proportions:

49/14 = (9*x + 1)/(x + 5)

Solving for x we get

49*(x + 5) = (9*x + 1)*14

49*x + 245 = 126*x + 14

245 - 14 = 126*x - 49*x

231 = 77*x

x = 231/77

x = 3

Ver imagen jbiain

The triangle JKL and triangle NMP are similar. so the ratio of the length of their sides is equal to each other and the measure of the length x is 3.

What are similar triangles?

If the two triangles are similar, the ratio of their sides and angles are in proportion.

Here, The triangle JKL and triangle NMP are similar. so the ratio of the length of their sides is equal to each other.

Then,

The ratio of the sides of the triangle is;

[tex]\rm \dfrac{49}{14} = \dfrac{(9\times x + 1)}{(x + 5)}\\\\ \dfrac{7}{2} = \dfrac{(9x + 1)}{(x + 5)}\\\\ 7(x+5)=2(9x+1)\\\\7x+35=18x+2\\\\18x-7x=35-2\\\\11x=33\\\\x=\dfrac{33}{11}\\\\x=3\\[/tex]

Hence, the measure of the length x is 3.

To know more about Triangle click the link given below.

brainly.com/question/25813512