In δabc, ab = 20 cm, ac = 15 cm. the length of the altitude an is 12 cm. prove that δabc is a right triangle.

Given : In ΔABC,AB = 20 cm, AC = 15 cm and the length of the altitude AN is 12 cm.

To prove: Triangle ABC is a right angled triangle

Proof:

Since AN is an altitude, so it is a line segment through a vertex and perpendicular to a line containing the base.

Consider the triangle ANB,

By Pythagoras theorem,

So, BN = 16 cm.

Consider the triangle ANC,

By Pythagoras theorem,

So, NC = 9 cm.

Therefore, BC = BN + NC = 16 + 9 = 25cm.

Now, consider

225 = 225

Therefore, By converse of Pythagoras theorem.

Triangle ABC is a right angled triangle.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11