SOLUTION: Find the diagonal of a rectangle with 5 in. width and 7 in. length

Question 109800: Find the diagonal of a rectangle with 5 in. width and 7 in. length
Found 2 solutions by kmcruz09, bucky:
Answer by kmcruz09(38) (Show Source): You can put this solution on YOUR website!
Basically, the line that bisects the rectangle is the line in the cartesian plane. It is simply the slope, rise over run.
Thank you.
~kmcruz09~
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If you sketch a rectangle that has a length of 7 inches and a width of 5 inches, and you then
draw in a diagonal, you will see that the diagonal splits the rectangle into two right triangles.
In both these triangles the diagonal is the long side, so it is the hypotenuse of each triangle,
and the two legs of each triangle are 5 inches and 7 inches.
.
Because the two triangles are right triangles, the Pythagorean theorem applies. This theorem
says that the sum of the squares of the two legs of a right triangle are equal to the square of
the hypotenuse of the triangle. In equation form this can be written as:
.

.
where A and B are the two legs of the right triangle and H is the hypotenuse. We can then
substitute 5 for one of the legs and 7 for the other to get:
.

.
Squaring out the two terms on the left side results in:
.

.
Adding the two terms on the left results in reducing the equation to:
.

.
You can then solve for the length of the hypotenuse (H) by taking the square root of both
sides to get that:
.

.
Calculator time ... the square root of 74 is 8.602325267. So the length of the hypotenuse is
8.602325267 inches, and this is the answer to your problem.
.
Hope this helps you to understand the problem a little better and to see a way that you can
solve it.
.

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