Sure! Let's find the length of the diagonal for a rectangle with sides of 10 inches and 20 inches.
1. Identify the given sides of the rectangle:
- Length [tex]\( a = 10 \)[/tex] inches
- Width [tex]\( b = 20 \)[/tex] inches
2. Recall the Pythagorean theorem for calculating the diagonal [tex]\( c \)[/tex] of a rectangle:
The Pythagorean theorem states that for a right triangle,
[tex]\[
c^2 = a^2 + b^2
\][/tex]
where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the two shorter sides, and [tex]\( c \)[/tex] is the length of the hypotenuse (or diagonal in this case).
3. Plug in the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the theorem:
[tex]\[
c^2 = (10)^2 + (20)^2
= 100 + 400
= 500
\][/tex]
4. Solve for [tex]\( c \)[/tex] by taking the square root of both sides:
[tex]\[
c = \sqrt{500}
\][/tex]
5. Comparison with given options:
Now, we compare the calculated diagonal length with the provided options:
- [tex]\( \sqrt{500} \)[/tex] inches.
- 30 inches.
- [tex]\( \sqrt{300} \)[/tex] inches.
- [tex]\( \sqrt{60} \)[/tex] inches.
Among the options provided, the length of the cut, which is the diagonal of the rectangle, is [tex]\( \sqrt{500} \)[/tex] inches.
Answer:
The length of the cut is [tex]\( \sqrt{500} \)[/tex] inches.
