Final answer:
The base of the triangle is approximately 1.348 inches.
Therefore, the correct answer is: option A) 1 inch
Step-by-step explanation:
To find the base of the triangle, we need to use the information given in the problem.
Let's assign the base of the triangle as 'b' and the height as 'h'.
According to the problem, the height is 2 inches more than three times the base, so we can write the equation :
h = 3b + 2.
The area of the triangle is given as 5 sq. in., so we can use the formula for the area of a triangle, which is Area = 1/2 * base * height, to write the equation 5 = 1/2 * b * (3b + 2).
Now, let's solve this equation to find the value of the base, b.
Simplifying the equation, we get 5 = 1.5b^2 + b.
Rearranging the terms, we have 1.5b^2 + b - 5 = 0.
To solve this quadratic equation, we can use the quadratic formula: b = (-b ± √(b^2 - 4ac)) / 2a.
Plugging in the values a = 1.5, b = 1, and c = -5, we get b ≈ -2.095 and b ≈ 1.348.
Since we are looking for a positive value for the base, the approximate value of the base is 1.348 inches.