What is the formula to calculate the diagonal measurement of a rectangle using only width and height?

Question

Specifically, I need the diagonal measurement of a 5' by 3' rectangle... but I'd like to know the formula as well, for future reference.

Answer 1

The formula is based on the Pythagorean theorem, because the diagonal cuts the rectangle into two right triangles. If you know the width, W, and the height, H, then the length of the diagonal is sqrt((W^2)+(H^2)). In this case, that's sqrt((5^2)+(3^2)) = sqrt(25+9) = sqrt(34).

Answer 2

use the Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the lengths of two legs, and c is the length of the diagonal. Hence, for your problem:

5^2 + 3^2 = c^2
25 + 9 = c^2
34 = c^2
c = square root of 34
c = 5.83 - the length of the diagonal of your rectangle

Answer 3

Let x= the short side
Let y= the long side
Let d= the diagonal
Then:
d= the square root of the sum of the squares of x and y
You will have a negative and a positive answer of the same value.
This occurs always when you solve for a square root.
In the example 5 squared + 3 squared= 25+9=34. The square root of 34 is 5.831 which is the answer to your problem.
You should use the common known mathematics symbols for square of the numbers and the square root to write the equation

Answer 4

Answer for your Question lies in Pythagoren theorem. Please ref the link.
if a and b are adjescent sides of a rectangle and c is diagonal

a^2 + b^2 = c^2

so c (diagonal ) is square root of (a^2 + b^2)

for the given problem answer is

c = Square root of (9+25) = 5.83.

http://mathworld.wolfram.com/PythagoreanTheorem.html

Answer 5

a^2 + b^2 = c^2
5^ + 3^2 = c^2
34^2 = c^2
take square root of 34^2 to find c
c = 5.83'

Answer 6

a. squared + b. squared = c. squared
a. 5' + b. 3' = c. 34 squared = 5.8309517
or
5ft. 9 and 31/32in.
or
69.97142 (69 and 31/32 inches)

.9375=15/16 Practical Fractional Inch
.96875=31/32
.97142=?
.984375=63/64

5x5=25 (a. squared)
3x3=9 (b. squared)
25+9=34 (c.)
34 squared=5.8309517 (c. squared)

Convert to inches
60"x60"=3,600sq.in. (a. squared)
36"x36"=1,296sq.in. (b. squared)
3,600+1,296=4,896sq.in. (c.)
4,896 squared=69.97142 (c. squared)

To calculate square root longhand (algorithm)
http://mathforum.org/library/drmath/view/52610.html

Answer 7

Pythagoras' formula.
c^2=a2+b^2
So your rectangle will be;
c^2=5^2+3^2
= 25+9
= 36
c = SQRT(36)
You can work that out...

Answer 8

pythagorean theorem d^2=l^2 + w^2

sqr root of (31)

Answer 9

d=sqrt(a^2+b^2)

in your case d=sqrt(25+9)
d=sqrt(34)

Answer 10

d=rt(h^2+w^2)
=rt(5^2+3^2)
=rt(34)
diagonal=rt34'