Question

Find the distance labeled x in the diagram. A. 20.8 ft B. 62.5 ft C. 35.0 t D. 42.5 ft​

Answer 1

Answer:

D) 42.5 ft

Step-by-step explanation:

Use ratios of base : height of the similar triangles:

largest triangle = (26 + 8) : x = 34 : x

smallest triangle = 8 : 10

Therefore,

$\dfrac{34}{x}=\dfrac{8}{10}$

Cross multiply:

$\implies 34 \times 10 =8x$

$\implies 340 =8x$

Divide both sides by 8:

$\implies x=42.5$

Answer 2

Solution:

Since the triangles are similar:

• 26 + 8:x = 8:10

Solving the equation:

• 34:x = 4:5
• => 34/x = 4/5
• => 34 x 5 = 4x
• => 170 = 4x
• => x = 170/4 = 42.5

The distance of x is 42.5 ft.