Use the given ratio and information in the figure to find the value of the variable(s).
XY:YZ:XZ=7:10:14
XY=b-7 These are side lengths
YZ=b+20 to a triangle. Side
XZ=5c-24 note XZ is the hypotenus
Need to show work
To find the value of the variable(s) in this problem, we can use the fact that the sum of the ratio terms is equal to the sum of the corresponding parts of the triangle.
The given ratio is:
XY:YZ:XZ = 7:10:14
We are also given the following information about the side lengths of the triangle:
XY = b - 7
YZ = b + 20
XZ = 5c - 24
To find the value of the variable(s), we need to set up an equation using the given ratio.
Add up the ratio terms:
7 + 10 + 14 = 31
This means that the sum of the lengths of XY, YZ, and XZ is equal to 31.
So, we can write the equation:
XY + YZ + XZ = 31
Substitute the given expressions for XY, YZ, and XZ:
(b - 7) + (b + 20) + (5c - 24) = 31
Now, we can solve this equation for the variable(s) b and c.
Combine like terms:
2b + 5c - 11 = 31
Bring the constant term to the other side of the equation:
2b + 5c = 42
This equation gives us a relationship between b and c, but it does not provide a specific value for either variable. To find the value(s), we need additional information or equations.