Question

Please solve. I need it for class right now.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:triangle=8.3\:unit^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt:\implies Hypotenuse(h) = 6 \: unit \\ \\ \tt:\implies Perpendicular(p) = 5 \: unit \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Area \: of \: triangle =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ \tt: \implies {6}^{2} = {5}^{2} + {b}^{2} \\ \\ \tt: \implies 36 - 25 = {b}^{2} \\ \\\tt: \implies {b}^{2} = 11 \\ \\ \tt: \implies b = \sqrt{11} \\ \\ \tt: \implies b = 3.3 \\ \\ \bold{As \: we \: know\:that} \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times Base \times Height \\ \\ \tt: \implies Area \: of \: triangle = \frac{1}{2} \times 3.3 \times 5 \\ \\ \tt: \implies Area \: of \: triangle =2.5 \times 3.3 \\ \\ \green{ \tt: \implies Area \: of \: triangle \approx 8.3 \: {unit}^{2} }$

Answer 2

$\huge{\yellow{\underline{\underline{ Given : }}}}$

$\:\:$

• $\tt{\blue{ Height = 5unit }}$

• $\tt{\blue{ Hypotenuse = 6unit }}$

$\:\:$

$\huge{\yellow{\underline{\underline{ To\: Find : }}}}$

$\:\:$

• $\tt{\orange{ Area\: of\: triangle }}$

$\:\:$

$\huge{\yellow{\underline{\underline{ Solution : }}}}$

$\:\:$

We know that hypotenuse² = Height ² + Base²

$\:\:$

Let, the base be x

$\:\:$

$\tt{\green{ {hypotenuse}^{2} = {height}^{2} + {base}^{2} }}$

$\tt{\green{\implies {(6unit)}^{2} = {(5unit)}^{2} + {(x)}^{2} }}$

$\tt{\green{\implies {36unit}^{2} = {25unit}^{2} + {x}^{2} }}$

$\tt{\green{\implies {36unit}^{2} - {25unit}^{2} = {x}^{2} }}$

$\tt{\green{\implies {11unit}^{2} = {x}^{2} }}$

$\tt{\green{\implies \sqrt{{11unit}^{2}} = x }}$

$\tt{\green{\implies 3.33unit = x }}$

$\:\:$

$\blue{\displaystyle{\tt{Area\:of\: Triangle = \frac{1}{2}\times base \times height }}}$

$\blue{\displaystyle{\tt{\implies Area\:of\: Triangle = \frac{1}{2}\times 3.33unit \times 5unit }}}$

$\blue{\displaystyle{\tt{\implies Area\:of\: Triangle = \frac{1}{2}\times {16.65unit}^{2} }}}$

$\blue{\displaystyle{\tt{\implies Area\:of\: Triangle = \frac{1}{\cancel{2}}\times {\cancel{16.65unit}^{2}} }}}$

$\blue{\displaystyle{\tt{\implies Area\:of\: Triangle = {8.3unit}^{2} }}}$

$\:\:$

$\blue{\displaystyle{\bf{ Area\:of\: Triangle = {8.3unit}^{2} }}}$