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Question
In square PQRS :
(i) if PQ = 3x – 7 and QR = x + 3 ; find PS
(ii) if PR = 5x and QS = 9x – 8. Find QS
Solution
(i) sides of square are equal.
PQ = QR
⇒ 3x – 7 = x + 3
⇒ 3x – x = 3 + 7
⇒ 2x = 10
x = 5
PS=PQ = 3x – 7 = 3 x 5 – 7 =8
(ii) PR = 5x and QS = 9x – 8
As diagonals of square are equal.
PR = QS
5x = 9x – 8
⇒ 5x – 9x = -8
⇒ -4x = -8
⇒ x = 2
QS = 9x – 8 = 9 x 2 – 8 =10
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