Algebraic word problems.

Question

A brand of crescent rolls are packaged in tubes that contain perforated triangles of dough. The base of the triangular piece of dough is about 5 cm more than its height. Determine the base and height of a piece of dough if the area is about 75 sq cm.

 

 

I have no idea how to solve this or any problems really. My teacher doesn't really teach. It is frustrating and I have no clue what to do. 

Answer 1

The area of a triangle is A = 1/ 2bh.  You can write the height as x and the base as x + 5 because it is 5 cm longer than the height.  Now, use the formula to solve for x:

 

A = 1/ 2bh

75 = 1/ 2(x + 5)(x)

75 = 1/ 2(x² + 5x)

150 = x² + 5x 

0 = x² + 5x - 150

 

Factor the trinomial:

 

x² + 5x - 150 = 0

(x + 15)(x - 10) = 0

 

Solve for your zeroes:

 

x + 15 = 0

x = -15

 

x - 10 = 0

x = 10

 

Because a length cannot be negative, x has to equal 10, so the height (x) is 10 cm and the base (x + 5) is 15 cm.