The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. Find the lenght of it's longest altitude.
Answers
Answer:
according to me 35 cm + 54cm + 61cm=159cm answer
Step-by-step explanation:
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✬ 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 ★
S = (35 + 54 + 61/2)
S = 150/2
S = 75 cm
★ Heron's Formula ∆ = √S (s – a) (s – b) (s – c) ★
Area of ∆ = √75 (75 – 35) (75 – 54) (75 – 61)
√75 x 40 x 21 x 15 cm²
√3 x 5 x 5 x 2 x 2 x 2 x 5 x 3 x 7 x 3 x 5 cm²
√15 x 15 x 14 x 14 x 4 x 5 cm²
(15 x 14 x 2) √5 cm²
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 ★
420√5 = 1/2 x 35 x h
(420 x 2 x √5/35) cm
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
