Question 252240: The sides of triangles A and B measure 5, 5, 8 and 5, 5, 6, respectively. What is the ratio of the area of triangle A to the area of triangle B ?
a. 1 : 1 b. 2 : 1 c. 3 : 2 d. 4 : 3 e. 5 : 4
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! Assume the base if given by the side that is 8 in triangle A and 6 in triangle B.
The area of a triangle is given by 
Since you already have the base for each triangle, what you need to find next is the height for each one.
Drop a vertical line from the corner of the triangle that is formed by the two 5 inch sides. That line will bisect the base and form two right triangles.
Use the Pythagorean theorem to find the height.
For Triangle A, the sides of the right triangle are 5,4,h. You know, or should memorize, that 3:4:5 ratio always forms a right triangle. So, the height for A is 3
Use the same logic on B, (5,3,h). Again, you have a 3:4:5, except this time the height is 4.
Now you have all the dimensions you need.
Find the ratio of the two areas as follows
So the ratio is 1:1
Wouldn't have figured that at first look. But the math doesn't lie.
Merry Christmas
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