Question

In a rectangle pqrs point t is outside the rectangle so that triangle ptq is a isosceles right angled triangle with hypotenuse pq if pq =4 and qr=3 find the area of triangle prt

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Answer 1

pqrs is a rectangle t is point out side the rectangle it form isosceles right triangle then angle qtp is 90

qtp is isosceles right triangle it means qt and tp is equal hence by phythagorus theorm qt square + tp square is equal to qp square

then 4

${4}^{2} = {x}^{2} + {x}^{2}$

since tp and qt are equal

then

${x}^{2} = 8$

x =

$\sqrt{2}$

now let a=

$2 \sqrt{2}$

and b=

$2 \sqrt{2}$

and c=

$4$

by herones formula= a+b+c/2

then it is equal to

$2(1 + \sqrt{2} ) = s$

now

$\sqrt{s(s - a)(s - b)(s - c)}$

putting value

and solve it

is give

$\sqrt{1 + 2 \sqrt{2} }$

hence it is ans