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zubka84 [21]
3 years ago
14

TUVW is a rectangle. Find the value of x and the length of each diagonal if

Mathematics
1 answer:
Alenkinab [10]3 years ago
4 0

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 <em>OR</em> 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

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