The side lengths of a rectangular room are 12 ft and 35 ft. The room is going to be split in half along the hypotenuse of a triangle using string. Find the length of the piece of string needed.

Question

12 ft
35 ft

A rectangle has side lengths of 12 feet and 35 feet. The rectangle is divided diagonally into two congruent triangles.
left parenthesis This figure is not drawn to scale. right parenthesis
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Part 1
The length of the piece of string needed is
  
enter your response here ft.
​(Simplify your​ answer.)

Answer 1

To find the length of the piece of string needed to divide the rectangular room along the hypotenuse of the triangle, we can use the Pythagorean theorem.

In the rectangle, the side lengths are 12 ft (height) and 35 ft (base). The diagonal (hypotenuse) can be found using the formula:

\[ c = \sqrt{a^2 + b^2} \]

where:

• \( c \) is the length of the hypotenuse,
• \( a \) is one side (12 ft),
• \( b \) is the other side (35 ft).

Now substituting the values:

\[ c = \sqrt{12^2 + 35^2} \] \[ = \sqrt{144 + 1225} \] \[ = \sqrt{1369} \] \[ = 37 \text{ ft} \]

Thus, the length of the piece of string needed is 37 ft.