Quadratics

Geometry Word Problem

 

Throughout this section, we will be learning how to apply our knowledge about quadratics to solve geometry problems. Please look below to see a sample problem that we will be analyzing:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANALYSIS: *Please refer below to see the steps taken to solve the sample geometry problem given above.*

 

Step 1: Set up let-statements. 

Step 2: Assign each side length of the triangle an expression. 

Step 3: Put the side-lengths in the form: a^2 + b^2 = c^2. 

Step 4: Expand and simplify.

Step 5: Make the c^2 side equal to 0, by cancelling out the value of c^2 with the value of a^2 + b^2. 

Step 6: Factor using the method of "simple trinomial factoring". 

Step 7: Set each factor to 0, to find the possible x-values.

Step 8: Pick the appropriate x-value.

Step 9: Substitute the appropriate x-value into the expressions for the side lengths to solve for the side lengths of the triangles.