Question

the base and height of a triangle are in the ratio 3:2 . if the area of the triangle is 243 cm square find the base and the height of the triangle

Answer 1

Area = 243
Take the base and height 3x and 2x
1/2 * b * h = 1/2 * 3x * 2x = 243
3x*2x = 243*2
x square = 243*2/6
x square = 81
x = 9
3x= 3*9=27 (base)
2x= 2*9=18(height)

Answer 2

$\; \star \; {\underline{\boxed{\pmb{\orange{\frak{ \; Given\; :- }}}}}}$

➺ Base = 3x

➺ Height = 2x

$\star \;{\underline{\boxed{\pmb{\red{\frak{ \; To \; Find \; :- }}}}}}$

➺ Base & Height = ?

$\; \star \; {\underline{\boxed{\pmb{\purple{\frak{ \; SolutioN \; :- }}}}}}$

$❒{\underline{\underline{\sf{ \; Calculating \: base \: and \: height \; \: : - }}}}$

${\underline{\underline{\sf{ \; Formula \; Used \; :- }}}}$

${ \underline{ \boxed {\sf{{Area_{(\triangle)}=\dfrac{1}{2}×base×height }}}}}$

${\longrightarrow \; {\sf{Area_{(\triangle)}=\dfrac{1}{2}×base ×height )}}} \;$

${\longrightarrow \; {\sf{243=\dfrac{1}{2}×3x×2x}}}$

${\longrightarrow \; {\sf{243=\dfrac{6x {}^{2} }{2}}}}$

${\longrightarrow \; {\sf{243 \times 2=6x {}^{2} }}}$

${\longrightarrow \; {\sf{486=6x {}^{2} }}}$

${\longrightarrow \; {\sf{ \dfrac{486}{6}=x {}^{2} }}}$

${\longrightarrow \; {\sf{ \cancel\dfrac{486}{6}=x {}^{2} }}}$

${\longrightarrow \; {\sf{ 81=x {}^{2} }}}$

${\longrightarrow \; {\sf{ \sqrt{ 81}=x }}}$

${\; \longrightarrow \; {{ \pink{ \underline{ \boxed{ \frak{ x=9}}}}}} }\;\red\bigstar$

$\begin{gathered} \\ \\ \end{gathered}$

$\therefore$Base of the triangle is 9×3=27cm and Height of the triangle is 9×2=18cm

$\begin{gathered}\begin{gathered}\begin{gathered} \\ {\underline{\rule{300pt}{9pt}}} \end{gathered} \end{gathered}\end{gathered}$