Question

perimeter
An isosceles triangle
has
30cm and each the equal is
12cm. Find the area
of the triangle​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Perimeter= 30cm
• In isosceles triangle two sides are equal =12cm

${\bf{\blue{\underline{Find:}}}}$

• Area of triangle

${\bf{\blue{\underline{Now:}}}}$

${\star \: { \boxed{\sf{ \purple{ \: semi \: perimeter \: of \: triangle = \frac{a + b + c}{2} }}}}} \\ \\ </p><p>$

Where,

• a=12
• b=12
• c=?
• semi-perimeter(s)=30/2=15

${\implies{\sf{ Perimeter = 12 + 12 + c }}}$

${\implies{\sf{ 30 = 12 + 12 + c}}}$

${\implies{\sf{ 30 = 24+ c}}}$

${\implies{\sf{ 30 - 24 = c}}}$

${\implies{\sf{ c = 6}}}$

${\star \: { \boxed{\sf{ \purple{ area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} }}}}}$

${\implies{\sf{ \sqrt{15(15 - 12)(15 - 12)(15 - 6)} }}}$

${\implies{\sf{ \sqrt{15(3)(3)(9)} }}}$

${\implies{\sf{ \sqrt{15(9)(9)} }}}$

${\implies{\sf{ 9 \sqrt{15} }}}$

Hence the Area of triangle is =9√15cm²

Answer 2

$\purple{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}$

$\rm{Perimeter \ of \ an \ isosceles \ triangle \ is \ 30 \ cm}$

$\rm{and \ it's \ two \ sides \ are \ of \ 12 \ cm.}$

$\rm{Find \ the \ area \ of \ the \ triangle}$

_________________________________________

$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\tt{\red{\star{\boxed{\green{\implies{ Area \ of \ triangle \ is \ = \ 9 \sqrt{15}}}}}}}$

_________________________________________

$\sf\large\underline\pink{Given:}$

$\rm{Perimeter \ of \ the \ isosceles \ triangle :}$

$\rm\implies{30 \ cm}$

$\rm{In \ isosceles \ triangle \ two \ sides \ are \ equal : }$

$\rm\implies{12 \ cm}$

_________________________________________

$\sf\large\underline\blue{To \ Find}$

$\rm{Area \ of \ the \ triangle }$

________________________________________

$\green{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}$

$\rm{We \ are \ given ,}$

$\rm{Perimeter \ of \ the \ isosceles \ triangle :}$

$\rm\implies{30 \ cm}$

$\rm{In \ isosceles \ triangle \ two \ sides \ are \ equal : }$

$\rm\implies{12 \ cm}$

$\rm{Let , \ p, \ q, \ and \ r \ be \ the \ sides \ of \ \triangle}$

$\rm{Where,}$

$\rm{p=12 , \ q=12}$

$\rm{We \ know,}$

$\rm{\green{\boxed{\star{\orange{ Semi \ perimeter \ \implies \frac{(p+q+r)}{2}}}}}}$

$\rm{But, \ we \ know}$

$\rm{Perimeter \ = \ 2 \times \ (Semi \ perimeter)}$

$\rm\therefore{Perimeter \ \implies \ ( \ p \ + \ q + \ r \ )}$

$\rm\therefore{30 \ \implies \ 12 \ + \ 12 \ + \ r}$

$\rm\therefore{30 \ \implies \ 24 \ + \ r}$

$\rm\therefore{r \ \implies \ 30 \ - \ 24}$

$\rm\therefore{r \ \implies \ 6}$

$\rm{\pink{\boxed{\star{\blue{ r \ \implies \ 6}}}}}$

$\rm{Now}$

${ \boxed{\bf{ \orange{ area \: of \: triangle = \sqrt{s(s - p)(s - q)(s - r)} }}}}$

${\therefore{\rm{ \sqrt{15(15 - 12)(15 - 12)(15 - 6)} }}}$

${\therefore{\rm{ Area\ of \ \triangle \ = \ \sqrt{15(3)(3)(9)} }}}$

${\therefore{\rm{ Area\ of \ \triangle \ = \ \sqrt{15(9)(9)} }}}$

${\therefore{\rm{ Area\ of \ \triangle \ = \ 9 \sqrt{15} }}}$

$\tt{\red{\star{\boxed{\green{\implies{ Area \ of \ triangle \ is \ = \ 9 \sqrt{15}}}}}}}$

___________________________________________

$\bf\orange{hope \ it \ helps \ :))}$