A retangle has a width of 9 units and a length of 40 units. what is the length of a diagnal?

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Work Shown:

See the diagram below.

A rectangle is cut along one of the diagonals to form two right triangles. Focus on just one of the triangles.

a = 9 and b = 40 are legs of the right triangle. The hypotenuse is some unknown value c.

Use the Pythagorean theorem to solve for c

a^2 + b^2 = c^2

9^2 + 40^2 = c^2

81 + 1600 = c^2

1681 = c^2

c^2 = 1681

c = sqrt(1681)

c = 41

The other diagonal is also 41 units long because every rectangle has both diagonals equal to one another.

41 units

Step-by-step explanation:

We can use the Pythagorean theorem

a^2+b^2 = c^2

We are looking for the diagonal, which is c the hypotenuse

9^2 + 40^2 = c^2

81+1600 = c^2

1681 =c^2

Taking the square root of each side

sqrt(1681) = sqrt(c^2)

41 = c

there are no answer choices

step-by-step explanation: