Question

27. Find the area of a triangle two sides of which are 18 cm & 10 cm & the perimeter is 42 cm
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Answer 1

Answer:

1/2×b×h

1/2×18×10

18×5

90

Step-by-step explanation:

may be the ans is 90

hope it's useful

Answer 2

$\large\underline\bold{ANSWER \red{\huge{\checkmark}}}$

$\pink{\overbrace{ \underbrace{ \red{\mid\star\mid \:\: \purple{ Area\:of\:triangle= 21\sqrt{ 11 }cm^2 } } \:\: \red{\mid\star\mid}}}}$

EXPLANATION IN DETAILS:-

$\large\underline\bold{GIVEN,}$

$\leadsto perimeter\:of\:triangle\:is\:= \blue{ 42cm} \\ \\ \leadsto two\:sides\:of\:triangle :- \\ \\ \leadsto a= \red{18cm } \\ \\ \leadsto b= \red{ 10cm} \\ \therefore \:we\:dont\: know\: \\ third\:side\:so\: let\:the\:third\:side\:be\:x\:cm \\ \\ \leadsto c=\red{x\:cm }$

$\large\underline\bold{TO\:FIND,}$

$\green{ \circ\: Area\:of\:triangle.}$

Using heron's formula

$\rm{ \boxed{ \underline{ \red{ A=\sqrt{s(s-a)(s-b)(s-c)} }}}}$

$\natural \: \text{ here we don't know the third side first } \\ \text{ finding third side then finding area of triangle .}$

$\large\underline\bold{SOLUTION,}$

$\therefore \:first\:finding\:third side \\ \\ \diamond \:\:perimeter \:of\:triangle= a+b+c \\ \\ \mid\implies 18+10+x= 42cm \\ \\ \mid\implies 28+x= 42cm \\ \\ \mid\implies x=42-28 \\ \\ \mid\implies x= 14 cm \\ \\ \red{ \underline{ \overline{ \mid\:\:c=14cm \:\:\mid}}}$

$\\ \\ \therefore we \:know \\ \\ \red{ \diamondsuit} \: \: s=\dfrac{a+b+c}{2} \:\: or\:\: s= \dfrac{perimeter\:of\: triangle}{2} \\ \\ \mid\leadsto s=\dfrac{42}{2} \\ \\ \mid\leadsto s= \cancel\dfrac{42}{2} \\ \\ \mid\leadsto s=21 \\ \\ \sf{ \boxed{ \blue{ \overline{\underline{ \mid\heartsuit\mid \: s= 21cm\: \mid\heartsuit \mid }}}}}$

$\\ \\ \clubsuit \: \: \blue{ Now\:using\:given\:formula \:finding\:area\:of\:triangle. }$

$\therefore \red{ A=\sqrt{s(s-a)(s-b)(s-c)}} \\ \\ \mid\implies \sqrt{ 21(21-18) (21-10) (21-14)} \\ \\ \mid\implies \sqrt{ 21(3)(11)(7)} \\ \\ \mid\implies \sqrt{21\times 21 \times 11} \\ \\ \mid\implies 21\sqrt{11} \\ \\ \mid\leadsto A=21\sqrt{11} cm^2$

$\rm{ \boxed{ \blue{ \overline{\underline{ \red{\mid\heartsuit\mid \: \: \green{Area\:of\:triangle= 21\sqrt{11}cm^2}\:\: \mid\heartsuit \mid }}}}}}$