If the diagonal of a square is 14in. what is the side length of the square?

Question

Algebra 2 help

Answer 1

diagonal=2^(1/2)*side

side=dia/2^(1/2)

side=14/2^(1/2)

2^(1/2)=1.414

I think so.....

Answer 2

Use the Pythagoras theorem...

In a right angled triangle of sides a and b.... and c being the side opposite the right angle then

a*2+b*2= C*2

(*2 means squared)

So the diagonal divides the square into two triangles.... the sides of the triangles are equal( it is a square getting divided...a square has equal sides).

Assuming A and B are the sides

A=B

Let C be the diagonal

So using the equation

A*2+B*2= C*2

A*2+A*2= 14 x 14

2 x(A*2)= 196

A*2= 196 / 2

A*2= 98

A= square root of 98 inches

A = 9.899 inches

You should know where to use the formulas

Answer 3

45-45-90 triangle.

By definition of a 45-45-90 triangle:

The diagonal = √2 * side of a leg, or the leg = diagonal/√2

diagonal = 14

Implies

leg = 14/√2 = 7√2

You can also prove this via Pythagorean theorem.

a² + b² = c²

but for a square a and b are the same length

a² + a² = c²

2a² = c²

a² = c²/2

or

a = √(c²/2) = c/√2

a = leg

c = diagonal

a = 14/√2 = 7√2