Question

The base of a triangle is 1 inch shorter than twice the height. The area of the triangle is 18 square inches. Find the base and the height of the triangle. Be sure to include the correct units.

a) Equation: Let the height of the triangle be "h" inches, and the base be "b" inches. We can write the equation for the area of the triangle as (1/2) * b * h = 18.
b) Base of the triangle: b = 2h - 1 inches
c) Height of the triangle: h = 7 inches
d) The base is 13 inches, and the height is 7 inches.

Answer 1

The student's question relates to finding the base and height of a triangle given the area and a relationship between the two dimensions. The base is found to be 13 inches, and the height 7 inches, by substituting the given relationship into the area formula and solving for the height first.

Step-by-step explanation:

The student is asking about finding the dimensions of a triangle given its area and a relationship between the base and height. We're given that the area is 18 square inches. The base b is 1 inch shorter than twice the height h (b = 2h - 1), and the area A of a triangle is given by the formula A = (1/2) * b * h. To find the base b and height h, we substitute b = 2h - 1 into the area formula and solve for h:

• (1/2) * (2h - 1) * h = 18
• h^2 - (1/2)h - 18 = 0
• Using the quadratic formula or factoring, we find h = 7 inches (ignoring the negative solution since height cannot be negative).
• Now, we can find b by substituting h into b = 2h - 1:
• b = 2(7) - 1 = 13 inches

Therefore, the base of the triangle is 13 inches, and the height is 7 inches.