Qstnid -A-4- In Square Pqrs : (I) If Pq = 3x - 7 And Qr = X + 3 ; Find Ps (Ii) If Pr = 5x And Qr = 9x - 8. Find Qs (I) If Pq = 3x - 7 And Qr = X + 3 ; Find Ps (Ii) If Pr = 5x And Qr = 9x - 8. Find Qs - 17: Special Types Of Quadrilaterals Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

17: Special Types of Quadrilaterals Class 8 Maths

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Qstn# A-4 Prvs-Qstn Next-Qstn

#4
In square PQRS : (i) if PQ = 3x - 7 and QR = x + 3 ; find PS (ii) if PR = 5x and QR = 9x - 8. Find QS (i) if PQ = 3x - 7 and QR = x + 3 ; find PS (ii) if PR = 5x and QR = 9x - 8. Find QS
Ans : (i) sides of square are equal.

PQ = QR
⇒ 3x - 7 = x + 3
⇒ 3x - x = 3 + 7
⇒ 2x = 10
⇒ x = 5
PS = PQ = 3x - 7 = 3×5 - 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 ×2 - 8 = 10 (i) sides of square are equal.

PQ = QR
⇒ 3x - 7 = x + 3
⇒ 3x - x = 3 + 7
⇒ 2x = 10
⇒ x = 5
PS = PQ = 3x - 7 = 3×5 - 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 ×2 - 8 = 10

#4-i
if PQ = 3x - 7 and QR = x + 3 ; find PS
Ans : sides of square are equal.

PQ = QR
⇒ 3x - 7 = x + 3
⇒ 3x - x = 3 + 7
⇒ 2x = 10
⇒ x = 5
PS = PQ = 3x - 7 = 3×5 - 7 =8

#4-ii
if PR = 5x and QR = 9x - 8. Find QS
Ans : 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 ×2 - 8 = 10