Final answer:
To find the base and height of the triangle, a quadratic equation is formed from the area formula and solved to yield the base of 16 yards and height of 23 yards.
Step-by-step explanation:
To solve the problem, let's denote the base of the triangle as 'b' yards. According to the problem, the height is 7 yards greater than the base; therefore, the height can be represented as 'b + 7' yards. The area of a triangle is calculated using the formula 1/2 × base × height. Given that the area of the triangle is 184 square yards, we can set up an equation: 1/2 × b × (b + 7) = 184.
Multiplying both sides of the equation by 2 to eliminate the fraction yields: b × (b + 7) = 368. Expanding the equation gives us a quadratic equation: b² + 7b - 368 = 0. Factoring this quadratic equation, we get: (b + 23)(b - 16) = 0. This gives us two possible solutions for the base, b = -23 or b = 16. Since the base cannot be negative, we discard b = -23, leaving us with the base b = 16 yards.
Now, to find the height, we substitute the base back into the height expression: Height = b + 7 = 16 yards + 7 yards = 23 yards. Therefore, the base of the triangle is 16 yards and the height is 23 yards.