Algebra 1 Word Problem QUIZ TOMORROW

Question

Find the Dimensions of the Triangle: (Hint: Area of Triangle = bh/2)

 

Area = 108 m^2

Height = x m.

Base = (x + 6) m.

Answer 1

Apply the algebraic expressions into the formula for the area of a triangle.

 

Area = (base)(height) / 2

 

108 = x(x + 6) / 2

 

 

Solve the bolded equation for x.

 

Multiply both sides of the equation by 2.

 

216 = x² + 6x

 

 

Subtract 216 on both sides of the equation.

 

0 = x² + 6x - 216

 

 

Factor using FOIL if possible.

 

0 = (x - 12)(x + 18)

 

 

x = 12         and         x = -18

 

 

Since we cannot have negative values for dimensions, we accept the positive value of x:

 

x = 12

 

 

This is your height.  Add this value to 6 to get your height.