Math, asked by cutie1689, 11 hours ago

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 mahanteshgejji
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

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