SOLUTION: The figure shows a right angled triangle where angle ACB=90�. Given that AB=(2x+1)cm, BC=2x cm and AC=(x-5) cm, 1) write down an equation in X, 2) find the value of X, 3) find

Question 1118980: The figure shows a right angled triangle where angle ACB=90�. Given that AB=(2x+1)cm, BC=2x cm and AC=(x-5) cm,
1) write down an equation in X,
2) find the value of X,
3) find the area of triangle ABC.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The right angle is at C, so AB is the hypotenuse. Then the Pythagorean Theorem says

x = 12 or x = 2

However, the solution x=2 gives a negative value for the length of one side of the triangle, so we choose the solution x=12. Then the sides of the triangle are
2x=24; x-5=7; 2x+1 = 25

The area of a right triangle is one-half the product of the lengths of the legs:
area = (1/2)(24)(7) = 84
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