Q7 of 14 Page 206

Find the length of the hypotenuse of an isosceles right-angled triangle having an area of 200 cm. Take √2 is equal to 1.414.

As given in the question, the triangle is right angled isosceles.


Isosceles means two sides having the same length.


Let the base of the triangle be of length a which implies altitude’s length also equal to a.


So we get AB = a cm and BC = a cm


Now by Pythogare’s Theorem we know that


(Hypotenuse)2 = (base)2 + (altitude)2


⇒ (AC)2 = (AB)2 + (BC)2


⇒ (AC)2 = a2 + a2


⇒ (AC)2 = 2a2


⇒ AC =


Also it is given that area of triangle is 200 cm2.


Now the area of right-angled triangle is given by


=


⇒


⇒


∴ Length of base = altitude = 20 cm.


Now Length of hypotenuse =


Length of hypotenuse =


= 20×1.414


= 28.28 cm


∴ Length of hypotenuse = 28.28cm.


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