The area of the numbered triangle on a shuffle board court is 27 ft2. Its height is 3 feet more than the length of the base. Find the length of the base and the height. Base ft Height ft

Base = 6ft

Height = 9ft

Step-by-step explanation:

Area of a triangle: 1/2 x base length x height

Base = b

Height = b+3

27 = 1/2 x b x (b+3)

27 / (1/2) = b (b+3)

54 = b^2 + 3b

0=b^2 + 3b - 54

Applying the quadratic formula

For: ax2 + bx + c

a=1; b=3; c = -54

x = [ - b ± √b²-4ac] / 2a

Replacing with the values given:

x = [ - 3 ± √ (3) ²-4 (1) - 54] / 2 (1)

x = [ - 3± √9 + 216] / 2

x = [-3 ± √225] / 2

x = [ - 3 ± 15] / 2

Positive:

x = [ - 3 + 15] / 2 = 12/2 = 6

b = 6 ft (base length)

Height = b+3 = 6+3 = 9 ft

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