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| Math Central | Quandaries & Queries |
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Subject: perimeter and area of a right angled triangle 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
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
You are going to need more information to determine the area of the triangle.
Penny
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