More Logical Than Mathematical(Geometrical I Should Say)
An isosceles triangle has sides with integer length. The sides of equal length are 2 units. Half the third one is more than 1.
What is the area of the triangle?
The answer is 1.9843.
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1 solution
Area of a triangle is given by sqrt(s(s-a)(s-b)(s-c)) where s = a+b+c/2 here s = 7/2 and the area comes to be sqrt7 * 3/4 = 1.98
This is a miscalculation. Because, if we were to use Heron's formula, we would need the semi-perimeter. The calculation and logic behind the side lengths is correct, but the perimeter is 7, not 8, and therefor the formula would be A=sqrt[(3.5)(.5)(1.5)^2]=1.984
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Thanks. I have updated the answer to 1.9843.
The mistake made in Rifath's calculation above is that the area should be
2 1 × 3 × 4 − ( 3 / 2 ) 2 = 4 3 7 = 1 . 9 8 4 3 . . . .
The area should be 1.9843
This is only an assumption. Other assumption is if the angles of triangle are 30, 30 and 120 degrees, then half of the third side is more than one i.e sqrt3. Hence the area of isosceles triangle is sqrt3. There may be many more solutions if the angles are varying.
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sorry forgot to say that (third side is an integer)
Answer should be 1.9843 !!! There is some problem with the answer which is being checked with. I cant understand how you got it correct. Taking into consideration that the 3rd side should be integer, which will only be true for 3 units.
I AM EXTREMELY SORRY FOR ALL THE TROUBLES I CAUSED
the answer is different if you find area using formula 0.5 base height
As same sides are 2 units,then the summation of the two sides is 2+2=4.So the length of the third sides should be from 1 to 3.Now if its 2 then it becomes equilateral,so it should be either 1 or 3.If its 1 then half the third on becomes 1/2,which doesn't satisfy the question.So the length of the third side is 3.That makes the area=2/4 * sqrt{4*(2)^2-3^2}=1/2 * sqrt 7=1.3229