Answer:
10.6 ft
Step-by-step explanation:
The complete question is:
The area of the triangle is 35 square feet. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth.Base=x+4 Height=x
SOLUTION:
As you know, Area of triangle 'A' = 1/2 x b x h
Where,
Base 'b' = x+4
Area 'A' = 35 ft²
Height 'h'= x
35 = (1/2)(x+4)x
35 =(x² + 4x)/2
2 * 35 =x² + 4x
70 = x² + 4x
x² + 4x - 70=0
Formula for the quadratic equation is
x = [- b ± √(b² - 4ac)]/2a
Where,
a=1, b= 4, c=-70
Plugging in the values.
x = [- 4 ± √4² - (4 × 1 × - 70)] / (2 × 1
)
x = [- 4 ± √(16 + 280)]/2
x = [- 4 ± √296]/2
x = (- 4 + 17.2)/2 or x = (- 4 - 17.2)/2
x = 13.2/2 or x = - 21.2/2
As, we choose to ignore negative value of 'x'
Therefore, x = 13.2/2 = 6.6
And, Length of the base will be:
x + 4 = 6.6 + 4 => 10.6 ft
