# The sides of cert

In a right angled triangle

(Hypotenuse) 2 = (Base)2 + (Height)2

where hypotenuse is the longest side.

(i) L.H.S. = (Hypotenuse)2 = (18)2 = 324

R.H.S. = (Base)2 + (Height)2 = (9)2 + (16)2 = 81 + 256 = 337

L.H.S. ≠ R.H.S.

It is not a right triangle.

(ii) L.H.S. = (Hypotenuse)2 = (27)2 = 729

R.H.S. = (Base)2 + (Height)2 = (7)2 + (25) 2 = 49 + 625 = 674

L.H.S. ≠ R.H.S.

It is not a right triangle.

(iii) L.H.S. = (Hypotenuse)2 = (5)2 = 25

R.H.S. = (Base)2 + (Height)2 = (1.4)2 + (4.8) 2 = 1.96 + 23.04 = 25

L.H.S. = R.H.S.

It is a right triangle.

(iv) L.H.S. = (Hypotenuse)2 = (4)2 = 16

R.H.S. = (Base)2 + (Height)2 = (1.6)2 + (3.8)2 = 2.56 + 14.44 = 17

L.H.S. ≠ R.H.S.

It is not a right triangle.

(v) L.H.S. = (Hypotenuse)2 = (a + 1)2

R.H.S. = (Base)2 + (Height)2 = (a-1)2 + (2√a)2 = a2 + 1-2a + 4a = a2 + 1 + 2a = (a + 1)2

L.H.S. = R.H.S.

It is a right triangle.

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