Question

If 5, 5r, 5r² are the lengths of the sides of a triangle, then r cannot be equal to:
(A) 3/4
(B) 5/4
(C) 7/4
(D) 3/2

Answer 1

Answer:

r ∉ 7/4.

Step-by-step explanation:

ΔPQR is possible if,

› 5 + 5r > 5r²

Divide 5 on both sides:

› 1 + r > r²

› r² - r - 1 < 0

Using quadratic formula -b±√b² - 4ac/2a we get,

› Roots to be 1 + √5/2, 1 - √5/2.

› (r - 1/2 + √5/2)(r - 1/2 - √5/2)

› r ∈ (-√5 + 1/2 , √5 + 1/2)

Solutions are:

› 3/4, 5/4, 3/2.

∵ 7/4 ∉ (-√5 + 1/2 , √5 + 1/2)

∴ r ∉ 7/4