Question

The height corresponding to the longest side of the triangle whose sides are 42 cm, 34 cm, and 20cm in length is:
a)15cm
b)36cm
c)16cm
d)None of these

Answer 1

⇝ Given :-

For A Triangle

• First Side = 42 cm

• Second Side = 34 cm

• Third Side = 20 cm

⇝ To Find :-

• The height corresponding to its longest side.

⇝ Solution :-

Here,

• First Side = a = 42 cm

• Second Side = b = 34 cm

• Third Side = c = 20 cm

Semi - Perimeter = s = $\bf\dfrac{42+34+20}{2}$ = 48 cm

❒ Finding Area :-

To Calculate Area when three sides are given we will use Heron's Formula which is :

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}$

where

• a , b and c are sides of Triangle

• s = Semi - Perimeter

⏩ Putting Values In Formula ;

$\small \rm Area = \sqrt{48(48-42)(48 - 34)(48-20) \: }$

$= \sqrt{48 \times 6 \times 14 \times 28 \:}$

$= \sqrt{112896}$

$\purple{ \large :\longmapsto \underline {\boxed{{\bf Area=336 cm^2} }}}$

We Know that Area is Also given by the formula :

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{Area = \dfrac{1}{2}\times Base \times Height }}}$

⏩ Taking Longest Side as Base :

Let height corresponding to its longest side = h

$\rm Area = \frac{1}{2} \times 42 \times h$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf Area = 21h \: c {m}^{2} } }}}$

⏩ Equating Both Calculated Areas :-

$:\longmapsto \rm 21h = 336$

$:\longmapsto \rm h = \cancel \frac{336}{21}$

$\green{ \Large :\longmapsto  \underline {\boxed{{\bf h = 16 \: cm} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{Required \: \text Height = 16 cm }}}}}$

Answer 2

Answer:

Given :-

• The height corresponding to the longest side of the triangle whose sides are 42cm,34cm and 20cm

○To find :-

• Here we should find the height corresponding to the longest side of triangle.

○Explanation :-

• Lets first take the given data in the question then we can answer the question.

• First side=x=42cm.
• Second side be=y= 34cm.
• Third side be=z=20cm.

♧If we want to find answer to your question we should take the semi perimeter value so,

• $s = \frac{42 + 34 + 20}{2}$
• $s = 48cm$

○Now ,

• Here we should find the area of triangle so here by using herons formula we get that,

• $area = \sqrt{s(s - x)(s - y)(s - x)}$
• By using this formula we get the value of area of triangle.

• $area = \sqrt{48(48 - 42)(48 - 34)(48 - 20)} = \sqrt{48 \times 6 \times 14 \times 28}$
• $area = \sqrt{112896}$
• $area = 336 {cm}^{2}$

○And,

• we know that area also can be calculated as

$area = \frac{1}{2} \times base \times height$

• Let height which is corresponding to its longest side be =h
• $area = \frac{1}{2} \times 42 \times h = area = 21hcm^2$

• Now by equating both of the areas we get that,

• $21h = 336$

• $h = \frac{336}{21}$
• $h = 16cm.$

○Therefore,

• The required answer be 16cm

○option C is the correct answer for your question.

Used formula :-

• Heron's formula we used to get the answer
• $area = \sqrt{s(s - x)(s - y)(s - z)}$
• And we also used,

• $area = \frac{1}{2} \times b \times h$

○Read for more information

• https://brainly.in/question/28610794.

• search on web.

○Hope it helps u mate .

○Thank you .