Question

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

Answer 1

Given :-

• First side of triangle (a) = 42 cm

• Second side of triangle (b) = 34 cm

• Third side of triangle (c) = 20 cm

To find :-

• The height corresponding to the longest side

Solution :-

s = a + b + c/2

➟ s = 42 + 34 + 20/2

➟ s = 96/2

➟ s = 48 cm

Now,

By using Heron's formula,

we know that,

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

Area = √48(48 - 42)(48 - 34) (48 - 20)

Area = √48 × 6 × 14 × 28

Area = √112896

Area = 336 cm²

Here, we know that, length of the longest side of triangle is 42 cm

Area of a triangle = ½ × b × h

➟ 336 = ½ × 42 × h

➟ 336 = 21 × h

➟ 336 = 21h

➟ $\rm\cancel\dfrac{336}{21}$ = h

➟ 16 = h

➟ h = 16 cm

Hence,the height corresponding to the longest side will be 16 cm.