contestada

oints Q and R are midpoints of the sides of triangle ABC.

Triangle A B C is cut by line segment Q R. Point Q is the midpoint of side A B and point R is the midpoint of side A C. The lengths of A Q and Q B are 4 p, the length of Q R is 2 p + 3, and the length of C B is 6 p minus 4. The lengths of A R and R C are congruent.

What is AQ?

10 units
14 units
20 units
32 units

Respuesta :

olayemiolakunle65

Answer:

AQ = 20 units

Step-by-step explanation:

Comparing triangle AQR to ABC,

[tex]\frac{AQ}{AB}[/tex] = [tex]\frac{QR}{BC}[/tex]

[tex]\frac{4p}{8p}[/tex] = [tex]\frac{2p + 3}{6p-4}[/tex]

cross multiply and make p the subject of formula, we have:

8p (2p+3) = 4p(6p-4)

16[tex]p^{2}[/tex] + 24p = 24[tex]p^{2}[/tex] - 16p

24p + 16p = 24[tex]p^{2}[/tex] - 16[tex]p^{2}[/tex]

40p = 8[tex]p^{2}[/tex]

divide through by 8p,

p = 5

Therefore, AQ = 4p

                        = 4 × 5

                        = 20

AQ = 20 units

Otras preguntas