In triangle PQR shown, point S (not shown)is on QR between Q and R. Give one possible value for the length of PS ...Explain your reasoning..
Triangle PQR = 13"
PQ = 6"
QR = 2"
PR = 5"
I need help in figuring this out this triangle with an equation or expression...thank you
The length of PS depends upon where S is located between Q and R. Draw the triangle. PS can have any length between PQ and PR. One possible value would be 5.5"
To determine a possible value for the length of PS, you can use the Triangle Inequality theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
In this case, you know that PQ = 6" and QR = 2". Therefore, the sum of these two sides is 6" + 2" = 8".
According to the Triangle Inequality theorem, PS must be less than 8".
Since you need just one possible value, you can assume that PS is equal to the difference between the sum of the other two sides and PR. Therefore, PS = (PQ + QR) - PR.
Using the given values for PQ, QR, and PR, you can substitute them into the expression:
PS = (6" + 2") - 5" = 8" - 5" = 3"
Therefore, one possible value for the length of PS is 3".
To find a possible value for the length of PS, we can use the triangle inequality theorem. This theorem states that in a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Using this theorem in triangle PQR, we have:
PQ + PR > QR
6" + 5" > 2"
11" > 2"
Since this statement is true, we can conclude that the triangle PQR is possible.
Now, since point S is on QR between Q and R, we know that PS + SQ + SR = PQ + QR + PR. We can substitute in the given values:
PS + SQ + SR = 6" + 2" + 5"
PS + SQ + SR = 13"
Since we are looking for a possible value for the length of PS, we can rearrange the equation to isolate PS:
PS = 13" - (SQ + SR)
Given the information provided, we do not have a specific value or any restrictions for the positions of points S, Q, and R. Therefore, there are multiple possible values for the lengths of SQ and SR, which would result in different values for PS.
For example, if we assume that SQ = 1" and SR = 2", then:
PS = 13" - (1" + 2")
PS = 13" - 3"
PS = 10"
So, one possible value for the length of PS is 10". However, keep in mind that this is just one example, and there are other valid combinations of SQ and SR that would yield different values for PS.