Question

The height of a triangle is 8 centimeters greater than half its base. The area of the triangle is 48 square centimeters what is the base length of the triangle

Answer 1

Answer:

base = 8 cm

height = 12 cm

Step-by-step explanation:

We will need the formula for area of a trianlge, which is

A = (1/2)bh    where b is the base, and h is the height

We are given two formulas...

"The height of a triangle is 8 centimeters greater than half its base" becomes

  h = (1/2)b + 8

"The area of the triangle is 48 square centimeters" becomes

48 = (1/2)bh

Plug the first formula into the second to solve for h

48 = (1/2)b[(1/2) + 8]             (h becomes (1/2)b + 8)

Now solve for b

48 = (1/4)b² + 4b

**This is a quadratic euquation.  Solve using factoring...

(1/4)b² + 4b - 48 = 0       (subtract 48 from both sides)

b² + 16b - 192  =  0       (multiply by 4 so b² is by itself, it's easier to factor this way)

Now factor...

(b + 24)(b - 8) = 0       (you need two numbers that add to 16 and multiply to -192)

Set each binomial equal to zero and solve for b

b + 24 = 0          

    b = -24    

**this anwser is not valid because b is a length, and you can't have negative length

b - 8 = 0

  b = 8        

Since the other solution is invalid, the base is b

If the base is b, then the height is...

h = (1/2)b + 8

 

   h = (1/2)(8) + 8

     h = 4 + 8

 

         h = 12