The diagonal of a square has a length of eight times begin square root two end square root cm. find the length of a side of the square. a. 8 cm b. 4 cm c. two times begin square root two end square root cm d. five times begin square root two end square root cm

ANSWER

A. 8cm

EXPLANATION

The diagonal of the square is

Let the length of each side of the square be l units.

Then the diagonal and any two sides form an isosceles right triangle with the diagonal being the hypotenuse.

We use the Pythagoras Theorem, to obtain,

This implies that,

Solve for l,

Take positive square root of both sides

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

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step-by-step explanation: