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Select the correct answer from each drop-down menu.
Square STQR is drawn on one side of right triangle TPQ.

The length of each side of the square is about __ units, and the length of its diagonal is about __ units.

Select the correct answer from each dropdown menu Square STQR is drawn on one side of right triangle TPQ The length of each side of the square is about units an class=

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calculista

Answer:

Part 1) The length of each side of the square is about 4.47 units

Part 2) The length of its diagonal is about 6.32 units

Step-by-step explanation:

Part 1)

Find the length of each side of the square

In the right triangle TPQ

Applying the Pythagoras Theorem

[tex]TQ^{2}=PQ^{2}-TP^{2}[/tex]

substitute the given values

[tex]TQ^{2}=6^{2}-4^{2}[/tex]

[tex]TQ^{2}=36-16[/tex]

[tex]TQ^{2}=20[/tex]

[tex]TQ=2\sqrt{5}\ units[/tex] -----> exact value

[tex]TQ=4.47\ units[/tex] -----> approximate value

Part 2)

Find the length of the diagonal of the square

Applying the Pythagoras Theorem

[tex]TR^{2}=TQ^{2}+QR^{2}[/tex]

we have

[tex]TQ=QR[/tex]

[tex]TQ=2\sqrt{5}\ units[/tex]

substitute

[tex]TR^{2}=(2\sqrt{5})^{2}+(2\sqrt{5})^{2}[/tex]

[tex]TR^{2}=40[/tex]

[tex]TR=2\sqrt{10}\ units[/tex] -----> exact value

[tex]TR=6.32\ units[/tex] ----> approximate value

KatelynS8001

Answer:

First box is 4.5 units and the second box is 6.3 units.

Step-by-step explanation: Correct Plato answer.

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