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

Algebra ->  Pythagorean-theorem -> 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       Log On


   

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) About Me  (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

%282x%29%5E2%2B%28x-5%29%5E2+=+%282x%2B1%29%5E2
4x%5E2%2Bx%5E2-10x%2B25+=+4x%5E2%2B4x%2B1
x%5E2-14x%2B24+=+0
%28x-12%29%28x-2%29+=+0

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