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pochemuha
3 years ago
12

A company is replacing cables with fiber optic lines in rectangular casing BCDE. If line segment DE = 3 cm and line 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

Mathematics
2 answers:
koban [17]3 years ago
5 0

Answer:

The smaller diameter is 4.24\ cm

Step-by-step explanation:

we know that

The diameter of the circle is equal to BD

Applying the Pythagoras Theorem

BD^{2} =BE^{2} +DE^{2}

substitute the given values

BD^{2} =3^{2} +3^{2}

BD^{2} =18

BD=4.24\ cm

shusha [124]3 years ago
3 0

Answer:

The correct option is C.

Step-by-step explanation:

Given information: BCDE is a rectangular casing, DE = 3 cm and BE = 3 cm.

We need to find the smallest diameter of pipe that will fit the fiber optic line. It means we have to find the measure of DB.

The measure of all interior angles of a rectangle or square is 90°.

\angle DEB=90^{\circ}

It means the DEB is right angled triangle.

According to the Pythagoras theorem:

hypotenuse^2=leg_1^2+leg_2^2

In triangle DEB,

(DB)^2=(DE)^2+(BE)^2

(DB)^2=(3)^2+(3)^2

(DB)^2=9+9

(DB)^2=18

Taking square root both sides.

DB=\sqrt{18}

DB=4.24264068712

DB\approx 4.24

Therefore the correct option is C.

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