SOLUTION: The sides of a triangular garden are 10 ft, 22 ft, and 18 ft. Is the garden in the shape of a right triangle? Justify your answer.

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Question 2522: The sides of a triangular garden are 10 ft, 22 ft, and 18 ft. Is the garden in the shape of a right triangle? Justify your answer.
Found 2 solutions by gsmani_iyer, kiru_khandelwal:
Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!

The sides of the triangle = 10 ft., 22 ft. & 18 ft.

If the triangle is a rt.angled triangle, then it hypotenus,
being the biggest side, should be = 22 ft.

Applying Pythagorus theorum, the square of hyp. should be equal
to the sum of the squares of the other two sides.

So 22%5E2should be = %2810%5E2+%2B+18%5E2%29
but here 484(Sq.of LHS) is not = 100 + 324.

So this triangular garden is not in the shape of rt.triangle. ... Proved.
gsm

Answer by kiru_khandelwal(79) About Me  (Show Source):
You can put this solution on YOUR website!
In a right angled triangle let the perpendicular length be p and base be b and hypotenuse be h
In a right angles triangle hypotonuese is the longest side and also
p^2 + b^2 = h^2.
SO in a traingle with sides 10, 22 and 18......the longest side 22 be the hypotenuese
so let h = 22
Now if (10)^2 + 18^2 = 22^2 then it will be a right angled triangle...
10^2 + 18^2 = 100 + 324 = 424
and
22^2 = 22*22 = 424
This implies that it is a right angled triangle :-)