puffley
03.03.2020 •
Mathematics
TUVW is a rectangle. Find the value of x and the length of each diagonal if
TV = 2x -4 and UW = x + 10.
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Ответ:
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 equalIts four vertices are right anglesIts diagonals equal each other and bisect each otherIn 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
Ответ: