Answer:
The value of x is 14
The length of each diagonal is 24 units
Step-by-step explanation:
Let us revise the properties of the rectangle
- Each two opposite sides are parallel and equal
- Its four vertices are right angles
- Its diagonals equal each other and bisect each other
In rectangle TUVW
∵ TV and UW are its diagonals
∴ TV = UW
∵ TV = 2x - 4
∵ UW = x + 10
- Equate them to find x
∴ 2x - 4 = x + 10
- Subtract x from both sides
∴ x - 4 = 10
- Add 4 to both sides
∴ x = 14
The value of x is 14
Substitute the value of x in the expression of TV OR UW to find the length of each diagonal
∵ TV = 2(14) - 4
∴ TV = 28 - 4
∴ TV = 24 units
The length of each diagonal is 24 units
