Question

A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 2.5 cm and segment BE = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth. 3.54 cm 3.91 cm 4.24 cm 4.95 cm

Answer 1

BD would be the hypotenuse of a right triangle, which would also be the diameter of the pipe.

Use the Pythagorean theorem:

BD = sqrt(2.5^2 + 3^2)

BD = sqrt(6.25 + 9)

BD = sqrt(15.25)

BD = 3.91 cm

Answer 2

Answer:

$\Huge \boxed{\mathrm{3.91 \ cm}}$

Step-by-step explanation:

The triangle BDE is a right triangle.

Line segment DE = 2.5 cm

Line segment BE = 3 cm

We can apply Pythagorean theorem to solve for the diameter of the pipe or the hypotenuse of the right triangle BDE.

$c=\sqrt{2.5^2 +3^2 }$

$c=\sqrt{15.25} = 3.90512483795...$

We can round up the length to nearest hundredth.

$3.90512483795 \approx 3.91$

The diameter of the pipe is 3.91 cm.