Answer:
C. 
Step-by-step explanation:
The Pythagorean Theorem express that right-angled triangles (see Figure) are described by the following expression:
(Choice D)
Where:
- Legs
- Hypotenuse
Equivalent forms of the equation are, respectively:
(Choice A)
(Choice B)
The choice C is not equivalent to the Pythagorean Theorem.
= 3x + 9x = 6x + 42
= 3x + 9x - 6x = 42 ( transposing +6x from LHS to RHS changes +6x to -6x )
= 12x - 6x = 42
= 6x = 42
= x = 42 ÷ 6 ( transposing ×6 from LHS to RHS changes ×6 to ÷6 )
= x = 7
Let us check whether we have found out the correct value of x or not by placing 7 in the place of x :
= ( 3 × 7 ) + ( 9 × 7 ) = 6 × 7 + 42
= 21 + 63 = 42 + 42
= 84 = 84
= LHS = RHS
Hence proved we have derived the correct value of x .
Therefore , the value of x = 7 .
The area of the triangle is 108
