Question

Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.
a)14√11
b)21√11
c)35√11
d)21√11

Answer 1

Answer:

d

Step-by-step explanation:

area of triangle √s（s -a）（s-b）（s-c）

a = 18cm

b= 10cm

semi perimeter =

s = 42 ÷ 2

s = 21 cm

p= 42 cm

a+b+c = 42

c= 42-28

c = 14 cm

replace with formula ↑

√21(21-18)(21-10)(21-14)

= √21(21)(11)

=21√11 cm²

Answer 2

⇝ Given :-

For A Triangle ;

• First Side = 18 cm

• Second Side = 10 cm

• Perimeter = 42 cm

⇝ To Find :-

• Area of the Triangle.

⇝ Solution :-

Here,

• First Side = a = 18 cm

• Second Side = b = 10 cm

• Perimeter = P = 42 cm

• Semi - Perimeter = s = $\bf\dfrac{42}{2}$ = 21 cm

❒ Finding Third Side :-

Let Third Side be = c

We Know,

$\rm Perimeter = Sum \: of \: All \: Sides$

$\rm:\longmapsto42 = 18 + 10 + c$

$\rm:\longmapsto c = 42 - 18 - 10$

$\purple{ \large :\longmapsto \underline {\boxed{{\bf c = 14 \: cm} }}}$

❒ 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 ;

$\small \rm Area = \sqrt{21(21 - 18)(21 - 10)(21 - 14) \: }$

$= \sqrt{21 \times 3 \times 11 \times 7 \: }$

$\purple{ \large :\longmapsto \underline {\boxed{{\bf Area=21\sqrt{11} \: cm^2} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{\text Area\:of\:\text Triangle = 21\sqrt{11} \: {cm}^{2} }}}}}$

Therefore ,

$\Large\underline{\green{\underline{\frak{\pmb{Option \: D \: is \: Correct}}}}}$