Question

In the diagram, PQRS is a rhombus with sides 3 cm. PQR and PSR are the two sectors of a circle with centers Q and S respectively.
Which of the following statements is false?

• (a) X is more than 3 cm from Q.

(b) X is less than 3 cm from S.

(c) X is equidistant from points P and Q.

(d) X is more than 3 cm from P.

Answer 1

Hint: Mathematics includes the study of topics which are related to quantity, structure, space and change. It has no generally accepted definition. Mathematics deals with a variety of numbers ranging from natural numbers to irrational numbers. In this problem we are given a rhombus with sides 3cm. By using the properties of rhombus, we can establish the relationship between length of diagonal and hence we can find a solution for this problem.

Complete step-by-step answer:
Mathematics is related to all the phenomena occurring in the world. When mathematical structures are good models of real phenomena mathematical reasoning can be used to provide insight or predictions about nature. One of the most important branches of mathematics is geometry. It includes the analysis of figures using simple theorems and results.

In our problem we are given a rhombus PQRS with a diagonal QS. A point X lies on the diagonal QS.


Since, X lies closer to the end S so it cannot be equidistant from points P and Q.

Also, by observation $QP>PX$ which provides evidence that X is less than 3 cm from P.

Hence, two options are false.

This implies that option (c) and option (d) are correct.

Note: The key step in solving this problem is the knowledge of geometrical figures, particularly rhombus. By using some properties and visual observation we can easily identify which statements are false with conclusive evidence. These observation skills will enhance the confidence of students.