Question

The length of the sides of a right angled triangle are three consecutive terms of a arithmetic sequence with common difference 2. Find the ares of the triangle.

Answer 1

Answer:

three sides of the triangle will be

x+2, x+4, x+6

since they are the sides of a right angle triangle

(x+6)^2=(x+2)^2 + (x+4)^2

x^2 +12x + 36 = x^2 +4x + 4 + x^2 +8x + 16

x^2- 2x^2 +36 - 20 = 0

x^2 = 16

x = 4

area of the triangle = (1/2)×(x+2)×(x+4)

=(1/2)×6×8= 24 Ans