Question

The area triangle is 35 square ft. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth. Base=x+4 Height=x

Answer 1

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 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