Question

In the given figure , what value of p will make ST parallel to QR ?

Answer 1

Answer:

p = 2

Step-by-step explanation:

By Basic Proportionality Theorem or Thale's Theorem,

(Since, in ΔPST & ΔPQR, sides ST & QR are parallel)

⇒ $\frac{PS}{SQ} = \frac{PT}{TR}$

⇒ $\frac{p}{3p+4} = \frac{p+3}{8p+9}$

⇒ p(8p+9) = (p+3)(3p+4)

⇒ 8p² + 9p = 3p² + 4p + 9p + 12

⇒ 5p² - 4p - 12 = 0

⇒ 5p² - 10p + 6p - 12 = 0

⇒ 5p(p-2) + 6(p-2) = 0

⇒ (5p+6)(p-2) = 0

⇒ p = -1.2, 2

But, (p = -1.2) is not possible since the length of a side cannot be negative.

So, p = 2

Hope this helps.....