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Answer the 15th question. { NO LINKS }.{ NO ANSWERS FROM GOOGLE }.

Q.15. If the perimeter of a right angled triangle is 60 cm and its hypotenuse is 25 cm, find its area.

The given right angled triangle is as under:

where the base is $x$ and the perpendicular is $y$

Since, hypotenuse is 25, thus using Pythagoras theorem,

${x}^{2}+{y}^{2}={25}^{2}\phantom{\rule{0ex}{0ex}}{x}^{2}+{y}^{2}=625.....\left(i\right)$

As, perimeter is 60, given in the question, therefore,

$x+y+25=60\phantom{\rule{0ex}{0ex}}x+y=35.....\left(ii\right)$

squaring both the sides, in equation (ii),

${\left(x+y\right)}^{2}={\left(35\right)}^{2}\phantom{\rule{0ex}{0ex}}{x}^{2}+{y}^{2}+2xy=1225$

Replacing the values of ${x}^{2}+{y}^{2}$ from equation (i),

$625+2xy=1225\phantom{\rule{0ex}{0ex}}2xy=600\phantom{\rule{0ex}{0ex}}xy=300$

Hence, area of the right angled triangle is;

$=\frac{1}{2}xy\phantom{\rule{0ex}{0ex}}=\frac{1}{2}\times 300\phantom{\rule{0ex}{0ex}}=150$

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