the length of the sides (in cm) of a right triangle are x, x+1 and x+2. find the length of the sides of the triangle. what is its area?
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Answer:
6 sq.units
Explanation:
By the Pythagoras theorem,
(x+2)2 = x2 + (x+1)2
x2+4x+4 = x2 + x2+2x+1
x2+4x+4 = 2x2+2x+1
0 = 2x2-x2 + 2x-4x +1-4
0 = x2 - 2x - 3
0 = x2 +x -3x -3
0 = x(x+1) - 3(x+1)
0 = (x+1)(x-3)
0 = x+1 0 = x-3
-1 = x. 3 = x
But length can't be negative.
therefore, x = 3
Area of triangle = 1/2*base*height
= 1/2*x*(x+1)
= 1/2*3*(3+1)
= 1/2*3*4
= 3*2
= 6 sq.units
Hence,area of triangle is 6sq.units.
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