The measures of the hypotenuse, leg 1 and leg 2 of the right triangle are 15, 12 and 9 units respectively.
The figure in the image is a right triangle.
From the image:
Hypotenuse = ( 3x + 3 )
Leg 1 = ( 3x - 3 )
Leg 2 = 3x
To determine the length of each side of the triangle, first, we solve for the value of x using the Pythagoras theorem.
( Hypotenuse )² = ( Leg )² + ( Leg 2 )²
Plug in the values:
( 3x + 3 )² = ( 3x - 3 )² + ( 3x )²
Solve for x:
( 3x + 3 )( 3x + 3 ) = ( 3x - 3 )( 3x - 3 ) + ( 3x )( 3x )
9x² + 9x + 9x + 9 = 9x² - 9x - 9x + 9 + 9x²
Collect and add like terms:
9x² + 18x + 9 = 18x² - 18x + 9
18x² - 9x² - 18x - 18x + 9 - 9 = 0
9x² - 36x = 0
9x( x - 4 ) = 0
9x = 0
x = 0
( x - 4 ) = 0
x - 4 = 0
x = 4
Therefore, the values of x are 0 and 4.
But we take x = 4 since we are dealing with dimensions:
Now we find the dimensions plugging in x = 4:
Hypotenuse = 3x + 3 = 3(4) + 3 = 12 + 3 = 15
Leg 1 = ( 3x - 3 ) = 3(4) - 3 = 12 - 3 = 9
Leg 2 = 3x = 3(4) = 12
Therfore, the measures are 15, 9 and 12 units.