Math, asked by adveya24, 1 year ago

The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. Find the lenght of it's longest altitude.

Answers

Answered by reet9372
2

Answer:

according to me 35 cm + 54cm + 61cm=159cm answer

Step-by-step explanation:

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Answered by pandaXop
13

Longest Altitude = 245 cm

Step-by-step explanation:

Given:

  • Measure of sides of triangle are 35 cm, 54 cm and 61 cm respectively.

To Find:

  • What is the measure of the length of its longest side i.e altitude?

Solution: Let the sides of triangle be a , b and c.

  • a = 35 cm
  • b = 54 cm
  • c = 61 cm

We have to find the area of this triangle by using Heron's formula

Semi Perimeter (S) = ( a + b + c/2 ) units

\small\implies{\sf } S = (35 + 54 + 61/2)

\small\implies{\sf } S = 150/2

\small\implies{\sf } S = 75 cm

Heron's Formula = S (s a) (s b) (s c)

\small\implies{\sf } Area of = 75 (75 35) (75 54) (75 61)

\small\implies{\sf } 75 x 40 x 21 x 15 cm²

\small\implies{\sf } 3 x 5 x 5 x 2 x 2 x 2 x 5 x 3 x 7 x 3 x 5 cm²

\small\implies{\sf } 15 x 15 x 14 x 14 x 4 x 5 cm²

\small\implies{\sf } (15 x 14 x 2) 5 cm²

\small\implies{\sf } 4205 cm²

Longest altitude will be on the smallest base of the triangle.

Let the longest altitude be h cm.

  • Base AD = 35 cm
  • Height CD = h cm

We know that area of triangle is also

Area of = 1/2 x Base x Height

\small\implies{\sf } 4205 = 1/2 x 35 x h

\small\implies{\sf } (420 x 2 x 5/35) cm

\small\implies{\sf } 245 cm.

___________________

Check

1/2 x Base x Height = 4205

1/2 x 35 x 245 = 4205

8405/2 = 4205

4205 = 4205

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