The height of a triangle is 4 ft less than the base x. The area is 126 ft2. Find the dimensions of the triangle.

Mathematics

1 answer:

valina [46]4 years ago

7 0

Answer:

Base = x = 18ft

Height = x - 4 = 14ft

Step-by-step explanation:

The formula for the area of A the triangle is given by the following equation:

1) A = (base * heigth)/(2)

From this problem, we know that

base = x and that the height is 4ft less than the base, so height = base - 4 = x - 4.

We also know that the area is 126ft², so A = 126 ft². Now we can replace these informations in equation 1).

126 = (x(x-4))/2

x² - 4x = 252

x² -4x - 252 = 0

The roots of this equation are x = 18 or x = -14. But we know that a triangle cannot have negative dimensions, so we use x = 18.

The base is x, so base = 18ft.

Height is 4ft less than the base, so height equals 18-4 = 14ft

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