Question

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

Answer 1

Answer:

$\huge \boxed{45}$

Step-by-step explanation:

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

$\displaystyle \sf \frac{MQ}{NP} =\frac{LQ}{LP}$

Let the length of LP be x.

$\displaystyle \frac{9}{27} =\frac{15}{x}$

Cross multiply.

$9x=15 \times 27$

$9x=405$

Divide both sides by 9.

$\displaystyle \frac{9x}{9} =\frac{405}{9}$

$x=45$

Answer 2

Answer:

LP = 45

Step-by-step explanation:

MQ/NP = LQ/LP

= 9/27

= 1/3

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