Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

✬ Longest Altitude = 24√5 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

$\small\implies{\sf }$ 420√5 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 ★

$\small\implies{\sf }$ 420√5 = 1/2 x 35 x h

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

$\small\implies{\sf }$ 24√5 cm.

___________________

★ Check ★

→ 1/2 x Base x Height = 420√5

→ 1/2 x 35 x 24√5 = 420√5

→ 840√5/2 = 420√5

→ 420√5 = 420√5