Question

If the perimeter of a square is 20, find the length of a diagonal. Round your answer to the nearest tenth.

7.7
7.1
6.3
8.4

Answer 1

option 2] 7. 1

Explanation:

Perimeter of square is 20.

therefore,

`perimeter \: = 4 * side \\ therefore \: 20 = 4 * side \\ \: \: \: \: \: \: side = (20)/(4) \: = 5`

the diagonal and the Two adjacent sides of the square form a right angle triangle, so,

By hypotenuse theorem,

`{iagonal}^(2) \: = {side1}^(2) + {side2 }^(2) \\ \: \: \: \: \: \: \: \: = {5}^(2) + {5 }^(2) \\ = 25 + 25....(as \: suare \: has \: equal \: sides \: i.e \: 5) \\ = 50 \\diagonal = √(50) \\ = √(25 * 2) \\ = 5 √(2 ) \\ = 5 * 1.414 \\ = 7.07 \\ = approx \: 7.1`

Answer 2

Since a square is equal on all 4 sides, that means each side would be 5, because 20/4=5

so using the Pythagorean thrm (which we can use since a square has all 90 degree angles)

a=5 b=5 c=?

5^2+5^2=c^2
25+25=c^2
50=c^2 *square root both sides*
c= 7.07

So the answer would be 7.1