Question

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

Answer 1

Answer:

$SU=3.5\ units$

Step-by-step explanation:

step 1

In the isosceles right triangle PQT

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

Applying the Pythagoras Theorem

we have

$PQ=PT =\sqrt{2}\ units$

$QT^{2}=PQ^{2} +PT^{2}$

substitute the values

$QT^{2}=\sqrt{2}^{2} +\sqrt{2}^{2}$

$QT^{2}=4$

$QT=2\ units$

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

$4^{2}=2^{2} +SU^{2}$

$SU^{2}=4^{2}-2^{2}$

$SU^{2}=12$

$SU=2\sqrt{3}\ units$

$SU=3.5\ units$