Answer:
Area A = 12 = 1/2 × x × (5x-2)
5x^2 - 2x -24 = 0
Solution;
Base x = 2.4
Height h = 10 ft
Step-by-step explanation:
Given;
base of the triangle is x feet;
Base = x
The height of a triangle is 2 less than 5 times it's base;
Height = 5x - 2
the area of the triangle is 12 square feet;
Area A = 12 ft^2
The area of a triangle is;
Area A = 1/2 × base × height
Substituting the base and height;;
Area A = 1/2 × x × (5x-2)
Area A = 1/2 × (5x^2 - 2x)
Area A = 12
12 = 1/2 × (5x^2 - 2x)
Multiply through by 2.
24 = (5x^2 - 2x)
5x^2 - 2x -24 = 0
Solving the simultaneous equation;
x = 2.4 or -2
Since the base cannot be negative;
x = 2.4 ft
Height h = 5x -2 = 5(2.4) - 2 = 12 - 2 = 10 ft
Base x = 2.4
Height h = 10 ft
