Question

PQR is a right angled triangle at Q and QS is perpendicular to PR. if PQ=6cm and PS=4cm find QS, RS and QR

Answer 1

QS = 2√5 cm
RS = 5 cm
QR = 3√5 cm

Answer 2

Answer:

$QS=2\sqrt{5}\text{ cm}$

$RS=5\text{ cm}$

$QR=3\sqrt{5}\text{ cm}$

Step-by-step explanation:

Give: PQR is a right angled triangle at Q and QS is perpendicular to PR. Please see the attachment for figure. If PQ=6cm and PS=4cm

To determine: QS, RS and QR

Calculation:

Using pythagoreous theorem, In ΔPQS, ∠S=90°

$PQ^2=PS^2+QS^2$

$6^2=4^2+QS^2$

$QS=\sqrt{36-16}=2\sqrt{5}\text{ cm}$

In ΔPQS, ∠S=90°

$\tan\theta =\frac{2\sqrt{5}}{4}$

In ΔPQR, ∠Q=90°

$\tan\theta =\frac{QR}{6}$

$\frac{QR}{6}=\frac{2\sqrt{5}}{4}$

$QR=3\sqrt{5}\text{ cm}$

Using pythagoreous theorem, In ΔRQS, ∠S=90°

$RQ^2=RS^2+QS^2$

$(3\sqrt{5})^2=RS^2+(2sqrt{5})^2$

$RS=\sqrt{45-20}=5\text{ cm}$