Question

If PQRS is a rectangle, find the length of QT

Answer 1

Step-by-step explanation:

Since, opposite sides of a rectangle are equal and each angle is of 90°.

$\therefore$ QP = RS = 14 cm

$In \:\triangle QPS, \: \angle QPS = 90\degree$

$\therefore \: QS= \sqrt{QP^2+ PS^2} \\ \therefore \: QS= \sqrt{(14)^2+ (20)^2 } \\ \therefore \: QS= \sqrt{196 + 400} \\ \therefore \: QS= \sqrt{596} \\ \therefore \: QS= 24.41 \: m$

$\because$ Diagonals of a rectangle bisects each other.

$\therefore\: QT = \frac{1}{2} QS\\\therefore\: QT = \frac{1}{2} \times 24.41\\\therefore\: QT =12.205\\\huge\orange {\boxed {\therefore\: QT =12.21\:m}}$