skyec Posts: 1, Reputation: 1 New Member #1 May 10, 2012, 05:44 PM
Diagonal of a quare is the square root of 20 feet what is the area of the square?
The diaganol of a square is the square root of 20 feet what is the area of the square?
 ebaines Posts: 12,131, Reputation: 1307 Expert #2 May 11, 2012, 05:46 AM
Originally Posted by skyec
The diaganol of a sqaure is the square root of 20 feet what is the area of the square?
You can apply the Pythagorian Theorem to find the length of a side of the square. Recall for a right triangle that a^2 + b^2 = c^2. In the case of a square side length a = side length b, and you have been told that c is sqrt(20), so:

$
2a^2 = ( \sqrt {20} )^2.
$

Solve for 'a', then use that to find the area of the square. Post back with your final answer and we'll check it for you.
 RPVega Posts: 29, Reputation: 2 New Member #3 Sep 25, 2012, 12:25 AM
First, always remember to draw a picture of the problem. In this situation, you
have a triangle with two equal sides, denoted by the variable x. Using the
Pythagorean (?) Theorem, we arrive at the equation below:

Equation #1: x**2 + x**2 = (20)**(1/2)

where "x**2" is x raised to the 2nd power, and "(20)**(1/2)" is 20 raised to the
1/2 power. (Recall that 20 raised to the 1/2 power is the same as taking the
square root of 20.)

We combine the two terms on the left side of the equal sign(=) of Equation #1
above, to get the following:

Equation #2: 2*(x**2) = (20)**(1/2)

Dividing BOTH sides of Equation #2 above, we get:

Equation #3: x**2 = [(20)**(1/2)]/2

But recall that the area, A, of a square is simply the square of one of its sides,
which we denote by the variable x, in this case. (Refer to the picture/diagram
that I asked you to draw.) This is shown below:

Area of Square = A = x*x= x**2

But Equation #3 above is also equal to x**2; therefore, the area of the square,
A, is equal to the right side of Equation #3:

A=x**2=[(20)**(1/2)]/2

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