Answer: x = 3
Explanation:
From the diagram above , the area of a triangle especially a right angled triangle
A = 1/2 X b X h where b is the base and h is the height.
Now,
h = x + 3
b = x + 1
Now , substitute for those values in the formula provided vide
A = 1/2 x (x+ 3)( x + 1 ) and equated it to 12
= (x+3)(x+1)
—————. = 12
2
Now, multiply both side a by 2 to make it a linear equation or better put , cross multiply
= (x+3)(x+1) = 2 x 12
= (x+3)(x+1) = 24
Then open the bracket by multiplication
= x2 + x + 3x + 3 = 24
= x2 + 4x + 3 = 24
= x2 + 4x + 3 - 24 = 0
By solving this quadratically,
= x2 + 7x - 3x - 21 = 0 ,
( x2 + 7x) - ( 3x - 21 ) = 0
x( x + 7 ) - 3( x + 7 ) = 0
Therefore
( x+ 7 )( x - 3 ) = 0
Solving this gives
x = -7 or x = 3
Therefore x = 3 since x can’t be negative, x can’t be = -7