Question

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.

Answer 1

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

Step-by-step explanation: Correct Plato answer.

Answer 2

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

Explanation:

Part 1)

Find the length of each side of the square

In the right triangle TPQ

Applying the Pythagoras Theorem

`TQ^(2)=PQ^(2)-TP^(2)`

substitute the given values

`TQ^(2)=6^(2)-4^(2)`

`TQ^(2)=36-16`

`TQ^(2)=20`

`TQ=2√(5)\ units` -----> exact value

`TQ=4.47\ units` -----> approximate value

Part 2)

Find the length of the diagonal of the square

Applying the Pythagoras Theorem

`TR^(2)=TQ^(2)+QR^(2)`

we have

`TQ=QR`

`TQ=2√(5)\ units`

substitute

`TR^(2)=(2√(5))^(2)+(2√(5))^(2)`

`TR^(2)=40`

`TR=2√(10)\ units` -----> exact value

`TR=6.32\ units` ----> approximate value