The sides of a triangle are 3 consecutive integers. A perpendicular is drawn on the second largest side. If it divides the second largest side into two parts of lengths p and q respectively, then find the value of (p - q)².
Answers
Answered by
0
Answer:
The value of (p - q)² = 16
Step-by-step explanation:
Let (x-1), x and (x+1) be the sides of a triangle.
AB = (x-1), BC = x and CA = x+1
Second largest side is BC
AD be the altitude drawn to BC.
BD = p and CD = q
∴ (p + q ) = x
In ΔABD
AD² = AB² - BD² ------ (1) [ from pythagorus thm]
InΔACD
AD² = AC² - CD² ------(2) [ from pythagorus thm]
From (1) and (2)
AB² - BD² = AC² - CD²
(x - 1)² - p² = (x + 1)² - q²
x² + 1 - 2x - p² = x² + 1 + 2x - q²
p² - q² = - 4x
(p +q) (p-q) = -4x
x (p-q) = -4x
(p-q) = -4
∴ (p-q)² = 16
Attachments:
Similar questions