Question

In ​ kite PQRS ​, TQ=3 cm and TP=4 cm. What is SP ? Enter your answer in the box.

Answer 1

Answer:5

Explanation:

Answer 2

Kite is a quadrilateral in which two disjoint pairs of consecutive sides are congruent

Given: In kite PQRS

where PR and SQ are the diagonals of Kite respectively as shown in the figure given below.

Given: TQ = 3 cm and TP = 4 cm

Let PR is the main diagonal and SQ is the cross diagonal of kite PQRS as shown in figure, also let T is the intersection point of PQRS.

By Property of Kite, diagonal SQ bisects PR at perpendicular angle i.e, 90 degree.

i,e

Then, in right angle ΔQTP

`PQ = √(TQ^2+TP^2)` [Using Pythagoras theorem]

Substitute the given values of TQ and TP we have;

`PQ = √(3^2+4^2) =√(9+16) =√(25) = 5 cm`

Also, PQ = SP [by definition of kite]

therefore, the side SP = 5 cm.