Question 131017
1.find perimeter of a square with diagonal of 12 centimeters

Let d be the lenght of every side of a square. then the perimeter = 4*d centimeters

Using Pythagoras Theorem, x^2+y^2 = z^2

where x=y=d and z = diagonal length = 12

d^2+d^2=12^2

2*d^2 = 144

d^2 = 144/2 = 72

so d = sqrt(72)

so perimeter = 4*sqrt(72)

2.find the diagonal of a square with a perimeter of 20 inches

since perimeter = 20, so each side of square  = 20/4 = 5 inches

Let d be the lenght of diagonal.

Using Pythagoras Theorem, x^2+y^2 = z^2

where x=y=5 and z=d

5^2+5^2 = d^2

d^2 = 25+25 = 50

sp d = sqrt(50) inches = length of diagonal

3.find the diagonal of a square with a perimeter of 28 inches

since perimeter = 28, so each side of square  = 28/4 = 7 inches

Let d be the lenght of diagonal.

Using Pythagoras Theorem, x^2+y^2 = z^2

where x=y=7 and z=d

7^2+7^2 = d^2

d^2 = 49+49 = sqrt(98)

sp d = sqrt(98) inches = length of diagonal