Final answer:
By setting up an equation using the area formula for a triangle with the given information, we find that the base of the triangle is 9 meters and the height is 4 meters.
Step-by-step explanation:
To solve for the base and height of the triangle when the base is 5 m longer than the height and the area is 18 m², we use the formula for the area of a triangle: area = ½ × base × height. Let the height of the triangle be 'h' meters. Therefore, the base will be 'h + 5' meters. Substituting the values into the area formula, we get:
18 = ½ × (h + 5) × h
Now, multiply both sides by 2 to eliminate the fraction which gives us:
36 = (h + 5)h
Simplify by expanding the right side:
36 = h² + 5h
This is a quadratic equation and can be rearranged as:
h² + 5h - 36 = 0
Factor the quadratic equation:
(h + 9)(h - 4) = 0
Thus, we have two possible values for h, which are -9 and 4. Since a height cannot be negative, we discard -9 and take h = 4 meters. Subsequently, the base is h + 5 which equals 9 meters. The base of the triangle is 9 meters and the height is 4 meters.