Question

Find the perimeter of a square is half a diagonal is equal to eight 

Answer 1

To find the perimeter of a square when half of its diagonal is equal to eight, we can use the following steps:

Let's assume the side length of the square is "s" and the length of the diagonal is "d". Since half of the diagonal is equal to eight, we have:

`\displaystyle (1)/(2)d=8`

Multiplying both sides by 2, we find:

`\displaystyle d=16`

In a square, the length of the diagonal is equal to
`\displaystyle √(2)s`. Substituting the value of "d", we have:

`\displaystyle 16=√(2)s`

To find the value of "s", we can square both sides:

`\displaystyle (16)^(2)=(√(2)s)^(2)`

Simplifying, we get:

`\displaystyle 256=2s^(2)`

Dividing both sides by 2, we find:

`\displaystyle 128=s^(2)`

Taking the square root of both sides, we have:

`\displaystyle s=√(128)`

Simplifying the square root, we get:

`\displaystyle s=8√(2)`

The perimeter of a square is given by 4 times the length of one side. Substituting the value of "s", we find:

`\displaystyle \text{Perimeter}=4* 8√(2)`

Simplifying, we get:

`\displaystyle \text{Perimeter}=32√(2)`

Therefore, the perimeter of the square is
`\displaystyle 32√(2)`.

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