Answer:
x = 8
Explanation:
You want the value of x for a right triangle with side lengths (x+1) and (x-3) and an area of 22.5 cm².
Triangle area
The area of a triangle is given by the formula ...
A = 1/2bh
Then the area of this triangle is ...
22.5 = 1/2(x -3)(x +1)
45 = x² -2x -3
48 = x(x -2) . . . . . . . add 3 and factor out x
We know that 48 can be factored as (8)(6). Comparing this to x(x-2), we see that x=8.
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Additional comment
x could also be -6, but that would make the side lengths be negative. The only applicable solution for this geometry is x=8.