Question

QRST is a square. PQ = 2√ RU = 4
What is the length of SU? Round to the nearest tenth.

Answer 1

`SU=3.5\ units`

Explanation:

step 1

In the isosceles right triangle PQT

PQ=PT ----> because is an isosceles triangle

Applying the Pythagoras Theorem

we have

`PQ=PT =√(2)\ units`

`QT^(2)=PQ^(2) +PT^(2)`

substitute the values

`QT^(2)=√(2)^(2) +√(2)^(2)`

`QT^(2)=4`

`QT=2\ units`

step 2

In the square QRST

`RS=QT=2\ units`

step 3

In the right triangle RSU

Applying the Pythagoras Theorem

`RU^(2)=RS^(2) +SU^(2)`

we have

`RU=4\ units`

`RS=2\ units`

substitute the values and solve for SU

`4^(2)=2^(2) +SU^(2)`

`SU^(2)=4^(2)-2^(2)`

`SU^(2)=12`

`SU=2√(3)\ units`

`SU=3.5\ units`