Answer:
Length of base is 17.2
Step-by-step explanation:
Area of triangle is (1/2)bh
Base is x+4
Area = 35sq ft
Height= x
35 = (1/2)bh
35 = (1/2)(x+4)x
35 = [(x+4)x]/2
Cross multiply
2 x35 = [(x+4)x]
70 = x^2+4x
0 = x^2+4x-70
Using quadratic formula
X= (-b_+sqrtb^2-4ac)/2a
b= 4
a=1
c=-70
X = (-4_+sqrt4^2-4(1)(-70)/2(1)
X= (-4_+sqrt16+280)/2
X= (-4_+sqrt296)/2
X = (-4_+17.2046505341)/2
X= (-4-17.2046505341)/2, (-4+17.2046505341)/2,
X = -21.2046505341, 13.2046505341
To the nearest tenth
X= -21.2 , 13.2
Length can not be negate so we disregard -21.2
Height is 13.2
Base is x+4 = 13.2 + 4 = 17.2
Answer: the length of the base is 10.6 ft
Step-by-step explanation:
The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
The area triangle is 35 square ft.
Base = x + 4
Height = x
Therefore,
1/2 × x × (x + 4) = 35
Multiplying both sides of the equation by 2, it becomes
x(x + 4) = 70
x² + 4x = 70
x² + 4x - 70 = 0
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1
b = 4
c = - - 70
Therefore,
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
Since x cannot be negative, then
x = 13.2/2 = 6.6
Length of the base is
x + 4 = 6.6 + 4 = 10.6 ft
