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

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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