Question

The diagram shows the measurements of 2 triangles in feet (ft). X Х 50 ft ) 125 ft K 30 ft M What is the value of x that proves the triangles above are similar?? (G.7)(1 point) O A. 75 ft O B. 12 ft O C. 60 ft D. 30 ft

Answer 1

Two triangles are similar when the corresponding angles are congruents and the corresponding sides are in proportion:

Then, you have the next corresponding sides:

JK and KL

TJ and LM

TK adn KM

To find the value of x that makes the corresponding sides TJ and LM be proportional, you use the next formula that shows the proportionaliti between the triangles TJK and KLM:

$\frac{JK}{KL}=\frac{TJ}{LM}=\frac{TK}{KM}$

As you know the measure of the sides JK and KL, you use that values, as follow:

$\frac{JK}{KL}=\frac{TJ}{LM}$$\frac{125ft}{50ft}=\frac{x}{30ft}$

Then, you clear the x:

$\frac{125ft\cdot30ft}{50ft}=x$

And calculate the value of x:

$x=\frac{3750ft^2}{50ft}=75ft$Then, the value of x that proves the triangles above are similar is x=75ft