Question

3. Show that the sides 5 cm, 12 cm and 13 cm
make a right angled triangle. Find the
length of the altitude on the longest side.​

Answer 1

Solution :-

Before solving we have to learn a theorem

It's Converse of pythagoras theorem

Converse of pythagoras theorem :- In a triangle, if sum of square of sides is equal square of 3rd side, then the angle opposite to 3rd side is right angle and the triangle is a right angled triangle.

Now, let's start solving

Sides of the triangle are 5 cm , 12 cm, 13 cm

Sum of squares of 2 sides = 5² + 12² = 25 + 144 = 169

Square of 3rd side = 13² = 169

i.e Sum of squares of 2 sides = Square of 3rd side

Therefore by Converse of pythagoras theorem the given triangle is a right angled triangle.

Find area of the triangle when AC is considered as base

• Base AB = 12 cm
• Height BC = 5 cm

Area of the ΔABC = 1/2 * Base * Height

= 1/2 * AB * BC

= 1/2 * 12 * 5

= 6 * 5 = 30 cm²

Now, consider AC longest side as base of the triangle

• Longest side = Base = AC = 13 cm
• Altitude on base = Height = BD

Area of the ΔABC = 1/2 * Base * height

⇒ 1/2 * AC * BD = 30 cm²

⇒ 13 * BD = 30 * 2

⇒ 13 * BD = 60

⇒ BD = 60/13 = 4.6 cm [ approx ]

Hence, the length of the altitude on the longest side is 4.6 cm.

Answer 2

Here is your answer user.