Question

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

Answer 1

Answer:

option 2] 7. 1

Step-by-step explanation:

Perimeter of square is 20.

therefore,

$perimeter \: = 4 \times side \\ therefore \: 20 = 4 \times side \\ \: \: \: \: \: \: side = \frac{20}{4} \: = 5$

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

By hypotenuse theorem,

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

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