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# Sides of a right angle triangle r in A.P.,if smallest side has length 2 units,find sumof other lengths?

7 years ago

h2 = a2 + b2 is only true for right-angled triangles. If all the angles of a triangle are less than 90° then h2 < a2 + b2 For example, in an equilateral triangle with sides 1 1 1 and all angles 60° 12 = 1 < 12 + 12 = 2 If one the angles of a triangle is greater than 90° then h2 > a2 + b2 Note that in any triangle, the longest side h cannot be longer than the sum of the other two sides. so h < a + b. If it equalled the sum of the other two then the triangle is just a line of length a + b = h! For example, if the two shorter sides of a right-angled triangle are 2 cm and 3 cm, what is the length of the longest side? If the longest side is h, then, by Pythagoras'' Theorem, we have: h2 = 22 + 32 = 13 h = √13 = 3·60555

solve by using this simple concept

7 years ago

LET ANOTHER TWO SIDES OF RIGHT ANGLED TRIANGLE ARE a,b.

BY THE GIVEN SUM

2,a,b ARE IN A.P.

2<a<b

therefore b is the hypotenus of the given right angled triangle

2a=2+b-------(1)

b=√(4+a^2)-----(2)

(2) in (1)

2a=2+√(4+a^2)

by solving

a=8/3

put a value in (1)

therefore b=10/3

sum of the remaining sides =a+b=6