Question

The length of a triangle
5 cm and 12 cm and 13 cm find the length of
perpendicular from the opposite vertex
to the side whose length is 13​

Answer 1

Given:

• The length of a triangle 5 cm and 12 cm and 13 cm.

To find:

• Find the length of perpendicular from the opposite vertex to the side whose length is 13?

Solution:

• Let's consider ABC is a triangle.

Where,

• Side of the triangle :
• A = 5cm
• A = 5cmB = 12cm
• A = 5cmB = 12cmC = 13cm

Here, Side :

• 5 + 12 + 13/2 = 30/2 = 15

• Let perpendicular of the triangle be p.

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, By using herons formula,

→ Area = √s(s - a)(s - b)(s - c)

→ √15(15 - 5)(15 - 12)(15 - 13)

→ √15(10)(3)(2)

→ √15(60)

→ √900

→ 30cm²

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Now, Let's find length of perpendicular,

→ ∆ = 1/2 × vertex × perpendicular.

→ 30 = 1/2 × 13 × p

→ p = 30 × 2/13

→ p = 4.61

∴ Hence, The length of perpendicular from the opposite vertex to the side whose length is 13 is 4.61.

Answer 2

Here, a=5

b=12

c=13

s= 1/2(a+b+c)

s=1/2(5+12+13)

s=1/2×30

s=15

Area of the triangle, A = s(s−a)(s−b)(s−c)

$\sqrt{s(s−a)(s−b)(s−c)}$

$\sqrt{15(15−5)(15−12)(15−13) }$

$\sqrt{15(10)(3)(2) }$

$\sqrt{900}$

A=30 cm

Let p be the length of perpendicular. Then,

A= 1/2×13×p

2A=13p

2×30=13p

P=60/13cm...