In rectangle PQRS, PR=18x-28 and QS=x+380. Find the value of x and the length of each diagonal.

17x = 408

x = 24

Gosnkasnhf

To find the value of x and the length of each diagonal in rectangle PQRS, we need to use the properties of a rectangle.

In a rectangle, opposite sides are congruent. Therefore, we know that PR is equal to QS.

Setting up an equation:

PR = QS
18x - 28 = x + 380

Now, let's solve this equation for x:

18x - x = 380 + 28
17x = 408
x = 408 / 17
x ≈ 24

Now that we have found the value of x, we can substitute it back into either PR or QS to find the length of each diagonal. Let's use PR:

PR = 18x - 28
PR = 18(24) - 28
PR = 432 - 28
PR = 404

So the length of each diagonal is 404 units.

Huh?

in a rectangle the diagonals are equal.

18 x - 28 = x + 380

17 x = 352
x = 20.7
etc