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A rectangle has side lengths, L and W, and a diagonal, d.
Complete the equations to answer the questions below.
How are L, W, and d related?
____^2 + ____^2 = ____^2
If L is 30 units long and W is 10 units long, how long is the diagonal to the nearest tenth?
d = ____ units
To relate the side lengths ( L ), ( W ), and the diagonal ( d ) of a rectangle, we can use the Pythagorean theorem. The equation is:
( L^2 + W^2 = d^2 )
Now, if ( L ) is 30 units and ( W ) is 10 units, we can find ( d ) as follows:
1. Substitute the values into the equation:
( 30^2 + 10^2 = d^2 )
2. Calculate the squares:
( 900 + 100 = d^2 )
3. Add the results:
( 1000 = d^2 )
4. To find ( d ), take the square root:
( d = sqrt{1000} )
5. Calculate the square root:
( d approx 31.6 ) units (to the nearest tenth).
So the answer is:
d = 31.6 units
This shows how to find the length of the diagonal based on the lengths of the sides of the rectangle! If you have more questions or need deeper understanding, feel free to ask or check the extended services page for more assistance.