Answer:
see explanation
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + (x + 1)² = 5² ← expand factor and simplify left side
x² + x² + 2x + 1 = 25 ( subtract 25 from both sides )
2x² + 2x - 24 = 0 ← divide through by 2
x² + x - 12 = 0 ← in standard form
(x + 4)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 3 = 0 ⇒ x = 3
However, x > 0 ⇒ x = 3
The legs of the right triangle are 3 and x+ 1 = 3 + 1 = 4
The area (A) of the triangle is calculated as
A = 0.5bh ( b is the base and h the height )
Here b = 3 and h = 4, thus
A = 0.5 × 3 × 4 = 0.5 × 12 = 6 units²
