The base of a triangle is three inches more than its height. If each is increased by 3 inches the
area of the triangle (1/2 bh)
is 14 square inches. Find the original base (đť‘Ź) and the original height
(â„Ž) in inches. (Lesson 15)
original b = h+3
(1/2)(b+3)(h+3) = (1/2)(h+6)(h+3) = 14
Now just solve for h, and then get b.
To solve this problem, we can start by setting up equations based on the given information.
Let's say the height of the triangle is h inches. According to the given information, the base of the triangle is 3 inches more than its height, which means the base can be represented as (h + 3) inches.
Now, with the given information that when both the base and height are increased by 3 inches, the area of the triangle is 14 square inches, we can set up the equation for the area of the triangle.
The area of the triangle is given by the formula: Area = (1/2) * base * height.
So, with the new dimensions, the area would be: (1/2) * (h + 3 + 3) * (h + 3) = 14.
Simplifying the equation, we have: (1/2) * (h + 6) * (h + 3) = 14.
Multiplying both sides of the equation by 2 to eliminate the fraction, we get: (h + 6) * (h + 3) = 28.
Expanding the equation, we have: h^2 + 9h + 18 = 28.
Rearranging the equation, we get the quadratic equation: h^2 + 9h + 18 - 28 = 0.
Simplifying further, we have: h^2 + 9h - 10 = 0.
Factorizing the equation, we get: (h + 10)(h - 1) = 0.
From here, we can see that h = -10 or h = 1. Since the height of a triangle cannot be negative, we discard the negative value.
Therefore, the original height of the triangle is h = 1 inch.
Since the base is 3 inches more than the height, the original base of the triangle would be: (1 + 3) = 4 inches.
So, the original base (b) of the triangle is 4 inches, and the original height (h) is 1 inch.