Question

Find the length of the diagonals of the isosceles trapezoid if AC = x + 1 and DB = 2x - 3

Answer 1

Isosceles trapezoid , diagonals are equal

AC = DB

x + 1 = 2x - 3

x = 4

So AC = DB = 4 + 1 = 5

Answer:

The length of the diagonals = 5

Answer 2

Each diagonal has a length of 5 units.

Explanation:

We know by given that side AD is equal to side BC.

Also, we know

`AC=x+1` and
`DB=2x-3`

Now, by definition, isosceles trapezoids have equal diagonals. So,

`AC=DB\\x+1=2x-3\\1+3=2x-x\\x=4`

Then, we replace the value of the variable in each expression to find the length of each diagonal

`AC=x+1=4+1=5\\DB=2x-3=2(4)-3=8-3=5`

Therefore, each diagonal has a length of 5 units.