Question

If MQ = 9, NP = 27, and LQ = 15, calculate the length of LP. Assume ΔLMQ ~ ΔLNP. Image not set to scale.

Answer 1

LP = 45

Explanation:

MQ/NP = LQ/LP

= 9/27

= 1/3

if LQ is 15 and is 1u, LP (3u) is 15 × 3 = 45

Answer 2

`\huge \boxed{45}`

Explanation:

We can solve by using ratios since the triangles are congruent.

`\displaystyle \sf (MQ)/(NP) =(LQ)/(LP)`

Let the length of LP be x.

`\displaystyle (9)/(27) =(15)/(x)`

Cross multiply.

`9x=15 * 27`

`9x=405`

Divide both sides by 9.

`\displaystyle (9x)/(9) =(405)/(9)`

`x=45`