The perimeter of triangle RXA is 39, PX=49 and AP=9.Find RX and RA.
P is at the middle.
I think it's under triangle bisector theorem. Help me answer this guys. Thanks
If the perimeter is 39, and P is inside RXA, there is no way that PX can be 49. That's greater than the sum of all the sides of the triangle!
To find the lengths RX and RA, we can start by applying the triangle bisector theorem. According to the theorem, if a line segment divides two sides of a triangle proportionally, then it is called a triangle bisector.
In this case, PX is the bisector of triangle RXA, with P as the midpoint of RX. We are given that PX = 49 and AP = 9.
Let's denote the length of RX as x. Since P is the midpoint of RX, the length of PX is also x.
According to the triangle bisector theorem, we can set up the following proportions:
PX / RX = AP / RA
Substituting the given values into the equation:
49 / x = 9 / RA
To solve for RA, we can cross-multiply:
9x = 49 * RA
Divide both sides by 9:
x = 49 / 9 * RA
Since PX = x, we know that PX = 49 / 9 * RA.
Now, we can use the perimeter of the triangle to set up another equation.
The perimeter of a triangle is the sum of the lengths of its three sides.
So, RX + RA + AX = 39
Since P is the midpoint of RX, RX = PX = 49.
Substituting these values into the perimeter equation:
49 + RA + AX = 39
Simplifying the equation:
RA + AX = 39 - 49
RA + AX = -10
Since AX = AP + PX = 9 + 49 = 58, the equation becomes:
RA + 58 = -10
Subtracting 58 from both sides:
RA = -10 - 58
RA = -68
However, it is not possible for a side length to be negative, so there seems to be a mistake or inconsistency in the given information or calculations.
Please double-check the values or recheck the problem statement for any errors.