The daigonals of a square is 42.5. Calculate the perimeter and area of square

Question

Perimeter and areas of square are to be found.. this topic is reakted to pythagoras theorem 

Answer 1

Hi Marwa.

 

Draw a square.  The draw a line through the center of the square from one corner to the opposite corner.  I wish I could draw this here for you...

 

What  you end up with is 2 right triangles.  And the diagonal is the hypotenuse.

 

Since a²+b²=c², and we know that c=42.5, and that a=b (because the legs are sides of a square), so we can rewrite this as

 

a²+a²=(42.5)²

 

or

 

2a²=1806.25

 

Divide both sides by 2

 

a² = 903.125

 

And take the square root of both sides.

 

a=30.052

 

 

So each side of your square is 30.052, and the perimeter is all four sides added together.

The area is legth x width, = (a) x (a)