Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm i

1.	Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. Find the height corresponding to the longest side.
Answer» Let a, b and c be the sides of a triangle. Apply Heron's Formula to find the area of triangle. Area = \(\sqrt{S(S-a)(S-b)(S-c)}\) Where S = \(\frac{a + b + c}{2}\) Here a = 42 cm, b = 34 cm and c = 20 cm S = (42 +34 +20)/2 = 48 Area = √(48(48-42)(48-34)(48-20)) = √(48 x 6 x 14 x 28) = 336 Area of triangle is 336 cm². Clearly, Length of longest side = 42 cm Also we know, Area of a triangle = 1/2 × Base × Height 336 = 1/2 × 42 × Height 336 = 21 x Height or Height = 16 The height corresponding to the longest side is 16 cm.

Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. Find the height corresponding to the longest side.

Answer»

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

Apply Heron's Formula to find the area of triangle.

Area = \(\sqrt{S(S-a)(S-b)(S-c)}\)

Where S = \(\frac{a + b + c}{2}\)

Here a = 42 cm, b = 34 cm and c = 20 cm

S = (42 +34 +20)/2 = 48

Area = √(48(48-42)(48-34)(48-20))

= √(48 x 6 x 14 x 28)

= 336

Area of triangle is 336 cm².

Clearly,

Length of longest side = 42 cm

Also we know, Area of a triangle = 1/2 × Base × Height

336 = 1/2 × 42 × Height

336 = 21 x Height

or Height = 16

The height corresponding to the longest side is 16 cm.