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 Subject: perimeter and area of a right angled triangle Name: naveen Who are you: Teacher Hey, I need to calculate the area of a right angled triangle. However the measurements of the 3 sides is missing. All we are told is that the perimeter of the triangle is 1000cm. Can somebody help me calculate the area as soon as possible. Thank you

Hi Naveen,

Knowing the perimeter only is not enough information to determine the area. For example if the triangle is an isosceles right triangle with equal sides of length x cm then Pythagoras theorem tells us that the length of the third side is √2 x. Since the perimeter is 100 cm

x + x + √2 x = 100

which gives x = 29.29 cm. The area of this triangle is

1/2 base height = 1/2 29.29 29.29 = 428.95 square centimeters.

Now suppose that you have a different right triangle where the base is twice the height. Let the height be h cm then the base is 2h cm and in this case Pythagoras tells that the length of the hypotenuse is √5 h cm. Again since the perimeter is 100 cm

h + 2h + √5 h = 100

which gives h = 19.1 cm. he area of this triangle is

1/2 base height = 1/2 (2 19.1) 19.1 = 364.81 square centimeters.

You are going to need more information to determine the area of the triangle.

Penny

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