Question

please give me write answer . ​

Answer 1

Answer:

Option (D)  AR > AQ is the correct answer.

Step-by-step explanation:

Given:

⇒ AP perpendicular to QR

⇒ PR greater than PQ

⇒ PS = PQ

To find out:

We have to find which one is the correct answer from the given options.

Solution:

(A) AP = QP

  From the figure, we can see that AP is greater than QP.  Therefore, option (A) is false.

(B) AP > AQ

   Consider the right angle triangle APQ, AQ is the hypotenuse of the triangle. We know that hypotenuse is the longest side of a right-angle triangle. Hence option (B) is false.

(C)  $\angle APS>\angle APQ$

        In the figure, it is shown that  $\angle APS=90^\circ$. Then the $\angle APQ$ must equal 90 degrees. Because these are linear pairs of angles. Hence, option (C) is false.

(D) AR > AQ

⇒  Consider the right-angle triangle APQ

   By Pythagorean theorem,

       AQ² = AP² + PQ²

⇒ Consider the right angle triangle APR

       AR² = AP² + PR²

              = AP² + (PS + SR)²

              = AP² + (PQ + SR)²

              = AP² + PQ² + 2.PQ.SR + SR²

We can see, here AR² > AQ² then AR > AQ. Hence option (D) is true.