Question

iii) The area of a right angled triangle is 50cm2

. If one of its legs measures 10 cm, then the length of the other

leg is

a)10 cm b) 15 cm c) 20cm d) 12cm​

Answer 1

☯ Question:-

The area of a right angled triangle is 50cm². If one of its leg's measure 10 cm, then the length of the other  leg is

a) 10 cm

b) 15 cm

c) 20 cm

d) 12 cm

☯ Solution:-

We know that,

$\star \: Area \: of \: triangle \: = \: \frac{1}{2} \times b \times h$

Let one of the given leg's be base(b). So, we have to find the value of 'h'.

$50 = \frac{1}{2} \times 10 \times h \: -----Substituting \: the \: given \: values$

$\frac{50 \times 2}{10} = h\\\\h = \frac{100}{10} \\\\\therefore \: h = 10 cm$

∴ height of the traingle = 10 cm

Answer 2

Given: The area of a right angled triangle is 50cm² and one of its legs (base) measure 10cm.

Need to find: The length of the other leg (height).

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⋆ DIAGRAM:

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf h}\put(2.8,.3){\large\bf 10\;cm}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf }\put(.8,.3){\large\bf }\put(5.8,.3){\large\bf }\end{picture}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\underline{\bf{\dag}{\frak{\;As\;we\;know\;that\;:}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\star\;\boxed{\pink{\sf{Area\;_{(triangle)}=\dfrac{1}{2}\times Base\times Height}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf{50=\dfrac{1}{2}\times 10\times h}\\\\\\:\implies\sf{50=5\times h}\\\\\\:\implies\sf{h=\dfrac{50}{5}}\\\\\\:\implies{\underline{\boxed{\purple{\frak{h=10\:cm}}}}}{\;\bigstar}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

${\underline{\sf{Hence,\:the\:length\:of\:the\:other\:leg\:is\:{\textsf{\textbf{10\;cm}}}}.}}$