SOLUTION: There are two triangles. One is XZY and the other is QRS. Triangle XZY has a height of 15 (ZW) and triangle QRS has a height of 8(RT). (The zw and rt are the names of the line (h)

Algebra ->  Triangles -> SOLUTION: There are two triangles. One is XZY and the other is QRS. Triangle XZY has a height of 15 (ZW) and triangle QRS has a height of 8(RT). (The zw and rt are the names of the line (h)       Log On


   

Question 1114153: There are two triangles. One is XZY and the other is QRS. Triangle XZY has a height of 15 (ZW) and triangle QRS has a height of 8(RT). (The zw and rt are the names of the line (h) going through the triangle). If the area of triangle QRS is 145 cm^2, find the area of triangle XZY.
Answer options:
1. 509.77
2. 513.26
3. 510.98
4. 503.94
My thinking process:
I got 509.77 as my answer but was not sure if it was correct or if I just guessed lucky. Thank you for your help in advance!
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
If B is the base for triangle XYZ
then %281%2F2%29B%2A15=areaOfXYZ.

If b is base for triangle QRS
then %281%2F2%29b%2A8=145 as given its area.
-
b%2A4=145
b=145%2F4
b=36%261%2F4

Assuming these are similar triangles, B=%2815%2F8%29b
B=%2815%2F8%29%28145%2F4%29
B=67.96875

Area of triangle XYZ:
%281%2F2%29%2A67.96875%2A15
highlight_green%28509.76563%29
or about 509.77.

NOT the only way to solve. There is a linear-to-area property for plane figures.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
As formulated and presented, this post makes no sense.