the perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. find its area
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Let ABC be a right angled triangle. Since , the perimeter of a right triangle = 60 cm
Thus,
AB + BC + CA = 60 cm
AB + BC + 25 = 60 cm
AB + BC = 60 - 25 = 35 cm ---------- i)
In ΔABC
Using Pythagoras theorem ,
(35)^2 - (25)^2 = 2 (AB) (BC)
(35 - 25) (35+25) = 2(AB) (BC)
(AB) (BC) = 300
⇒ Area of right angle ABC = 150cm^2
Thus,
AB + BC + CA = 60 cm
AB + BC + 25 = 60 cm
AB + BC = 60 - 25 = 35 cm ---------- i)
In ΔABC
Using Pythagoras theorem ,
(35)^2 - (25)^2 = 2 (AB) (BC)
(35 - 25) (35+25) = 2(AB) (BC)
(AB) (BC) = 300
⇒ Area of right angle ABC = 150cm^2
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