SOLUTION: What is the area of a rectangle with a length of 45 and diagonals of 51?

Question 118667: What is the area of a rectangle with a length of 45 and diagonals of 51?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If we cut the rectangle in half along the diagonal, we get this triangle

Since we can see that the triangle has legs of x and 45 with a hypotenuse of 51, we can use Pythagoreans theorem to find the unknown side.

Pythagoreans theorem:

where a and b are the legs of the triangle and c is the hypotenuse

Plug in a=x, b=45, and c=51. Now lets solve for x

Square each individual term

Subtract 2025 from both sides

Combine like terms

Take the square root of both sides

Simplify the square root

So the width is 24

Now multiply 24 and 45 to get the area

So the area of the rectangle is 1080

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