Question

the sides of a triangle area 42cm,32cm and 20cm.find it's area and length of the height on the longest side
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Answer 1

Answer:

Step-by-step explanation:

Given :-

Sides of triangle = 42 cm, 32 cm and 20 cm

Solution :-

Let side a = 42 cm, b = 34 cm and c = 20 cm

Semiperimeter = (42 + 34 + 20)/2 = 48 cm

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

Area of triangle = √[ 48 × 6 × 14 × 28 ]   cm²  

Area of triangle = 336 cm²

Altitude on the base of 42 cm = h

⇒ 336 = 1/2 × 42 × h

⇒ h = 16 cm

Hence, it's area is 336 cm² and length of the height on the longest side is 16 cm.

Answer 2

Answer:

→ 336 cm² = area.

→ 16 cm = length ( Longest side ).

Explanation:

→ 42 + 34 + 20 / 2 = 48 cm.

→ 48 cm = Semi - Perimeter.

Hence:

$= \sqrt{s(s - a)(s - b)(s - c)} = area \: of \: triangle. \\ = \sqrt{48 \times 6 \times 14 \times 28 =} \:area \: of \: triangle.$

→ 42 cm = height of the base.

→ 336 = 1/2 × 42 × h

→ h = 16 cm

Therefore , 336 cm² = area and 16 cm = length ( Longest side ).