The area of the numbered triangle on a shuffle board court is 27 ft^2.

Its height is 3 feet more than the length of the base. Find the length of the base and the height.

Area of a triangle = 1/2 * base * height

Its height is 3 feet more than the base.

Let's substitute "b + 3" for the height so we only have one variable to solve for.

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

Let's multiply by 2 to get rid of the 1/2.

54 = b * (b + 3)

Distribute.

54 = b² + 3b

Multiple ways to solve this: You could guess and check ...

If b = 5 then we'd have 25 + 15 = 40

If b = 6 then we'd have 36 + 18 = 54 - - > base = 6 feet

Then, putting b = 6 into our equation with the height ...

27 = 1/2 * b * h

54 = 6 * h

height = 9 feet

Or you could factor and solve the quadratic. (Algebra I concept)

b² + 3b - 54 = 0

We want two numbers that multiply to equal - 54 and add to equal 3.

-54 = - 6 * 9

3 = - 6 + 9

Split the milddle ...

b² - 6b + 9b - 54 = 0

Factor the first and last two pairs of terms.

b (b-6) + 9 (b-6)

(9+b) (b-6) = 0

Any value of b which causes either factor to equal 0 is a solution.

9 + b = 0 or b - 6 = 0

b = - 9 or b = 6

Since b is a side length, it can be only positive.

base = 6 feet

Then you wouldl use that b = 6 in an earlier equation to find h = 9.