Question

How long would a piece of wood need to be to make a diagonal brace for a rectangle that measures 4 inches by 3 inches? Use the Pythagorean theorem, a² + b² = c², to determine the answer. 5 inches 7 inches 12 inches 25 inches Select the correct answer.

Answer 1

Length of a diagonal = 5 inches

Step-by-step explanation:

Let
`a` and
`b` the sides of the rectangle and
`c` be the diagonal of the rectangle.

According to the Pythagorean theorem, sum of squares of base and perpendicular is equal to the square of hypotenuse.

As each angle of the rectangle is a right angle,

`a^2+b^2=c^2`

Put
`a=4\,,\,b=3`

`4^2+3^2=c^2\\16+9=c^2\\25=c^2\\√(25)=c\\ 5=c`

So,

Length of a diagonal = 5 inches