Question

Find the area of the triangle whose sides are 42cm,34cmand 20cm in length.Hence,find the height corresponding to the longest side.
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Answer 1

Answer:

area = 336cm2 and h = 16cm

Step-by-step explanation:

s= 42+34+20/2

s=96/2=48

By heron 's formula

Area=√48(48-42)(48-34)(48-20)

=√48*6*14*28

=√2*2*2*2*3*2*3*2*7*2*2*7

=336cm2

height = area *2/side

= 336*2/42

=16cm

Answer 2

Answer

• Height , h = 16 cm

Given

• Sides of a triangle are 42 cm,34 cm and 20 cm in length

To Find

• Height of the triangle

Formula

Heron's Formula

$\bullet \;\; \rm \sqrt{s(s-a)(s-b)(s-c)}\\\\\rm where,\;\; s=\dfrac{a+b+c}{2}$

$\bullet \;\; \rm Area\ of\ triangle\ =\dfrac{1}{2}\times b \times h$

where ,

• b denotes base of the triangle
• h denotes height of the triangle

Solution

a = 42 cm

b = 34 cm

c = 20 cm

$\implies \rm s=\dfrac{a+b+c}{2}\\\\\implies \rm s=\dfrac{42+34+20}{2}\\\\\implies \rm s=\dfrac{96}{2}\\\\\implies \rm s=48\ cm$

Apply Heron's formula for finding area of the triangle .

$\implies \rm \sqrt{s(s-a)(s-b)(s-c)}\\\\\implies \rm \sqrt{48(48-42)(48-34)(48-20)}\\\\\implies \rm \sqrt{48 \times 6 \times 14 \times 28}\\\\\implies \rm 336\ cm^2$

Now we need to find the height corresponding to the longest side .

⇒ Base , b = 42 cm

Area of Δ = 336 cm²

Height , h = ? cm

$\implies \rm \dfrac{1}{2}\times b \times h=336\\\\\implies \rm \dfrac{1}{2} \times 42 \times h=336\\\\\implies \rm 21 \times h =336\\\\\implies \rm h=16\ cm$