Answer:
56
Step-by-step explanation:
Data
Area of a triangle = base*height*1/2
If we take AB as a base, CX is the height, but if we take AC as a base, BY is the height. Therefore:
AB*CX*1/2 = AC*BY*1/2
Replacing with data:
CX = 70*60/75
CX = 56
Answer:
56
Step-by-step explanation:
The area of $\triangle ABC$ is half the base times the height. We can use any side as a base, with the perpendicular from the opposite vertex as the matching height.
Using $AC$ as a base, the area of $\triangle ABC$ is $\frac{AC\cdot BY}{2} = \frac{70\cdot 60}{2} = 2100$.
Using $AB$ as a base, the area of $\triangle ABC$ is $\frac{AB\cdot CX}{2} = \frac{75\cdot CX}{2}$. We already know that this is $2100$, so we can set up the equation
$\frac{75\cdot CX}{2} = 2100.$Solving this equation, we get
$CX = \frac{2\cdot 2100}{75} = \boxed{56}.$
