Question

if the sides of a triangle are 13cm, 5cm. 12cm.,find the length of the altitude corresponding to the longest side as base

Answer 1

$13 + 5 + 12 = 30$
answer is 30cm


:-)

Answer 2

Step-by-step explanation:

Answer:

Altitude of triangle is 60/13 cm.

Step-by-step explanation:

We will use Heron's formula here, beacuse we do not have height of triangle.

Heron's formula is '

Area of triangle = √s(s - a)(s - b)(s - c)

Where,

s is semi-perimeter of triangle.

a, b and c are sides of triangle.

Semi - Perimeter of triangle = Perimeter/2

$\longrightarrow⟶ Semi-perimeter = 13 + 5 + 12/2$

$\longrightarrow⟶ Semi-perimeter = 30/2$

$\longrightarrow⟶ Semi-perimeter = 15$

Semi-perimeter of triangle is 15 cm.

We will find area :

$\longrightarrow⟶ Area = √15(15 - 13)(15 - 5)(15 - 12)$

$\longrightarrow⟶ Area = √15 × 2 × 10 × 3$

$\longrightarrow⟶ Area = √5 × 3 × 2 × 2 × 5 × 3$

$\longrightarrow⟶ Area = 2 × 3 × 5$

$\longrightarrow⟶ Area = 30$

Area of triangle is 30 cm².

Now,

Let, Height/altitude of triangle be h.

13 cm is longest side of triangle. So, If we take base 13 cm and height/altitude of triangle be h then area of triangle will same.

So,

Area of triangle = ½ × base × height

$\longrightarrow⟶ 30 = ½ × 13 × h$

$\longrightarrow⟶ 30 × 2 = 13 × h$

$\longrightarrow⟶ 60 = 13 × h$

$\longrightarrow⟶ 60/13 = h$

Altitude of triangle is 60/13 cm.