Question

DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal.

Answer 1

The length of the diagonal is
1) 4
2) DF = 15
3) EG= 15

Answer 2

Part a)
`x=4`

Part b)
`DF=EG=15\ units`

Explanation:

Step 1

Find the value of x

we know that

In a rectangle the length side of the two diagonals is the same

so

In this problem

`DF=EG`

substitute the values

`5x-5=x+11`

solve for x

`5x-x=11+5`

`4x=16`

`x=4`

Step 2

Find the length of the diagonal

`DF=EG=5x-5=5(4)-5=15\ units`