Q14 of 99 Page 267

If the perimeter of an isosceles right-angled triangle is (√2+1) cm. Let us write by calculating the length of hypotenuse and area of triangle.

Given, Perimeter of isosceles right angled triangle = (√ 2+1)cm


Let the equal sides of the isosceles triangle = a cm


Then the hypotenuse = a√ 2 cm


According to the given condition


a+ a + √ 2 a = (√ 2+1)


⇒ 2a+ √ 2 a = (√ 2+1)


⇒ a (2+√ 2) = (√ 2+1)


⇒


By rationalizing the denominator




Here, In denominator a = 2 and b = √2



= cm


Now hypotenuse = a√ 2


⇒ Hypotenuse


⇒ Hypotenuse = 1cm


Area = 1/2 base × height


Here hypotenuse is the height of the right isosceles triangle


Area =


= cm2


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