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Question
Find the length of the hypotenuse of an isosceles right-angled triangle whose area is `200^2` cm . Also, find its perimeter
Solution
In a right isosceles triangle, base = height = a
Therefore,
`Area of a triangle=1/2xxbasexxheight=1/2xxaxxa=1/2a^2`
Further, given that area of isosceles right triangle=`200cm^2`
⇒`1/2a^2=200`
⇒`a^2=400`
Or,` a=sqrt400=20cm`
In an isosceles right triangle, two sides are equal ( 'a`) and the third side is the hypotenuse,
i.e, 'c'
Therefore, `C=sqrt(a^2+a^2)`
=`sqrt(2a^2)`
=`asqrt2`
=`20xx1.41`
=`28.2 cm`
Perimeter of the triangle=` a+a+c`
=`20+20+28.2`
=`68.2cm`
The length of the hypotenuse is 28.2 cm and the perimeter of the triangle is 68.2 cm.
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