in a rhombus PQRS PQ=y+8, QS=4y-7.Find PQ
To find the length of PQ in the rhombus PQRS, given that PQ = y + 8 and QS = 4y - 7, we need to use the properties of a rhombus.
In a rhombus, opposite sides are congruent, which means that PQ = RS and QS = PR.
Since PQ = RS, we can set up an equation:
PQ = RS
y + 8 = RS -- (Equation 1)
Similarly, since QS = PR, we can set up another equation:
QS = PR
4y - 7 = PR -- (Equation 2)
Now, remember that opposite sides of a rhombus are congruent. Therefore, we can set Equation 1 equal to Equation 2:
y + 8 = 4y - 7
To solve this equation, we'll isolate the variable y on one side:
8 + 7 = 4y - y
Simplifying, we have:
15 = 3y
Next, to solve for y, we divide both sides of the equation by 3:
15/3 = 3y/3
5 = y
Now that we have the value of y, we can substitute it back into the expression for PQ:
PQ = y + 8
PQ = 5 + 8
PQ = 13
Therefore, the length of PQ in this rhombus is 13.