Question

The base of a right-angled traingle measures 48 cm and its hypotenuse measures 50 cm . Find the area of the traingle.

with full solution please​

Answer 1

$\frak{Given}\begin{cases}\sf{\;\;\;Base\;of\;the\;triangle=\frak{48\;cm}}\\\sf{\;\;\;Hypotenuse\;of\;the\;triangle=\frak{50\;cm}}\end{cases}$

$\frak{To\;find:}$ Area of the triangle?

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$\underline{\pink{\mathcal{\bigstar\;BY\;USING\;PYTHAGORAS\;THEOREM\;:}}}$

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$\begin{gathered}:\implies\sf{(AC)^2=(AB)^2+(BC)^2}\\\\\\:\implies\sf{(50)^2=(AB)^2+(48)^2}\\\\\\:\implies\sf{2500=(AB)^2+2304}\\\\\\:\implies\sf{2500-2304=(AB)^2}\\\\\\:\implies\sf{196=(AB)^2}\\\\\\:\implies\sf{AB=\sqrt{196}}\\\\\\:\implies\underline{\boxed{\frak{\pmb{AB=14\;cm}}}}\;\bigstar\end{gathered}$

$\therefore\;{\underline{\textsf{Hence,\;the\;height\;of\;the\;triangle\;is\;{\textbf{14\;cm}}}.}}$

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As we know that,

To calculate the area of a right-angled triangle formula is given by :

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$\qquad\star\;\underline{\boxed{\sf{\pmb{Area\;_{\triangle}=\dfrac{1}{2}\times Base\times Height}}}}$

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Therefore,

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$\begin{gathered}\twoheadrightarrow\sf{\;\dfrac{1}{2}\times 48\times 14}\\\\\\\twoheadrightarrow\sf{\;(48\times 7)\;cm^2}\\\\\\\twoheadrightarrow\;\underline{\boxed{\frak{\pmb{\purple{336\;cm^2}}}}}\;\bigstar\end{gathered}$

$\therefore\;{\underline{\sf{Hence,\;the\;area\;of\;the\;triangle\;is\;\bf{336\;cm^2}.}}}$⠀⠀⠀

Answer 2

Given : The base of a right-angled traingle measures 48cm & its hypotenuse measures 50cm.

To Find : Find the area of the traingle ?

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Solution : Let the area of the triangle be x.

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$\underline{\frak{As~ we ~know ~that~:}}$

• $\underset{\blue{\bf Pythagoras\ Theorem}}{\underbrace{\boxed{\sf{\pink{(Hypotenuse)^2~=~(Perpendicular)^2~+~(Base)^2}}}}}$

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$\pmb{\sf{\underline{According ~to~ the~ Given~ Question~:}}}$

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$\qquad{\sf:\implies{(50)^2~=~(48)^2~+~(H)^2}}$

$\qquad{\sf:\implies{2500~=~2304~+~H^2}}$

$\qquad{\sf:\implies{196~=~H^2}}$

$\qquad{\sf:\implies{H~=~\sqrt{196}}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{\pmb{H~=~14~cm}}}}}}$★

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Therefore,

• Height of triangle is 14cm.

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FINDING AREA :

• $\boxed{\sf\pink{Area_{\triangle}~=~\dfrac{1}{2}~×~Base~×~Height}}$★

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$\pmb{\sf{\underline{Substituting~ the ~Given ~Values~:}}}$

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$\qquad{\sf:\implies{Area_{\triangle}~=~\dfrac{1}{\cancel{2}}~×~14~×~\cancel{48}}}$

$\qquad{\sf:\implies{Area_{\triangle}~=~14~×~24}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{Area_{\triangle}~=~336~cm^2}}}}}}$★

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Hence,

$\therefore\underline{\sf{The ~area ~of~ the~\triangle~ is~\bf{\underline{\pmb{336~cm^2}}}}}$