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.