Final answer:
By using the area formula for a triangle, Area = 1/2 × base × height, and the given conditions, we derive a quadratic equation which upon solving reveals the base to be 13 inches and the height to be 8 inches.
Step-by-step explanation:
To solve this problem, we need to utilize the formula for the area of a triangle, which is given by Area = 1/2 × base × height. Given that the height of the triangle is five inches less than the length of its base, we can set up an equation to represent this relationship.
Let the base be represented by 'b' and the height by 'h'. We are told that h = b - 5 inches. The area of the triangle is given as 52 square inches. Substituting the expressions for base and height into the area formula, we get:
52 = 1/2 × b × (b - 5)
To find the base, we need to solve this quadratic equation. Multiplying both sides by 2 to clear the fraction, we get:
104 = b × (b - 5)
Distributing the 'b' we get:
104 = b2 - 5b
Moving all terms to one side results in:
b2 - 5b - 104 = 0
Factoring this quadratic equation, we find:
(b - 13)(b + 8) = 0
Since base cannot be negative, 'b' must be 13 inches, which makes the height 'h' equal to 13 - 5 = 8 inches. Thus, the correct answer is Base = 13 inches, Height = 8 inches.