In square PQRS : (i) if PQ = 3x - 7 and QR = x + 3, find PS. (ii) if PR = 5x and QS = 9x — 8. Find QS.

(i) In a square PQRS, all sides are equal and all angles are 90°. Thus, PQ = QR = PS = RS. It is given that PQ = 3x \- 7 and QR = x \+ 3. ⇒ (3x \- 7) = (x \+ 3) ⇒ 3x \- 7 = x \+ 3 ⇒ 3x \- x = 7 \+ 3 ⇒ 2x = 10 ⇒ x = ⇒ x = 5 Now, substitute the value of x = 5 into the expression for PQ: PQ = QR = PS = RS = (3x \- 7) = (3 5 \- 7) = (15 \- 7) = 8 Hence, the length of PS = 8 units. (ii) In a square PQRS, all sides are equal and all angles are 90°. Thus, PQ = QR = PS = RS. It is given that PR = 5x and QS = 9x - 8. ⇒ (5x) = (9x \- 8) ⇒ 5x = 9x \- 8 ⇒ 9x \- 5x = 8 ⇒ 4x = 8 ⇒ x = ⇒ x = 2 Now, substitute the value of x = 2 into the expression for PQ: PQ = QR = PS = RS = 5x = 5 2 = 10 Hence, the length of QS = 10 units.

In parallelogram PQRS, ∠Q = (4x - 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.

View Answer Bookmark Now

In rhombus ABCD :
(i) if ∠A = 74°, find ∠B and ∠C.
(ii) if AD = 7.5 cm, find BC and CD.

View Answer Bookmark Now

ABCD is a rectangle. If ∠BPC = 124°, calculate :
(i) ∠BAP
(ii) ∠ADP.

View Answer Bookmark Now

ABCD is a rhombus. If ∠BAC = 38°, find :
(i) ∠ACB
(ii) ∠DAC
(iii) ∠ADC.

View Answer Bookmark Now

Mathematics

In square PQRS :
(i) if PQ = 3x - 7 and QR = x + 3, find PS.
(ii) if PR = 5x and QS = 9x — 8. Find QS.

Quadrilaterals

Related Questions

In parallelogram PQRS, ∠Q = (4x - 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.

In rhombus ABCD :
(i) if ∠A = 74°, find ∠B and ∠C.
(ii) if AD = 7.5 cm, find BC and CD.

ABCD is a rectangle. If ∠BPC = 124°, calculate :
(i) ∠BAP
(ii) ∠ADP.

ABCD is a rhombus. If ∠BAC = 38°, find :
(i) ∠ACB
(ii) ∠DAC
(iii) ∠ADC.

Mathematics

In square PQRS :(i) if PQ = 3x - 7 and QR = x + 3, find PS.(ii) if PR = 5x and QS = 9x — 8. Find QS.

Quadrilaterals

Related Questions

In parallelogram PQRS, ∠Q = (4x - 5)° and ∠S = (3x + 10)°. Calculate: ∠Q and ∠R.

In rhombus ABCD :(i) if ∠A = 74°, find ∠B and ∠C.(ii) if AD = 7.5 cm, find BC and CD.

ABCD is a rectangle. If ∠BPC = 124°, calculate :(i) ∠BAP(ii) ∠ADP.

ABCD is a rhombus. If ∠BAC = 38°, find :(i) ∠ACB(ii) ∠DAC(iii) ∠ADC.

In square PQRS :
(i) if PQ = 3x - 7 and QR = x + 3, find PS.
(ii) if PR = 5x and QS = 9x — 8. Find QS.

In rhombus ABCD :
(i) if ∠A = 74°, find ∠B and ∠C.
(ii) if AD = 7.5 cm, find BC and CD.

ABCD is a rectangle. If ∠BPC = 124°, calculate :
(i) ∠BAP
(ii) ∠ADP.

ABCD is a rhombus. If ∠BAC = 38°, find :
(i) ∠ACB
(ii) ∠DAC
(iii) ∠ADC.