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Standard VIII

Mathematics

Construction of a Quadrilateral When Three Sides and Two Included Angles Are Given

Construct a q...

Question

Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, $∠ Q = 45^{\circ}$ and $∠ R = 90^{\circ}$ .

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Solution

Steps of Construction :

(i) Draw a line segment QR = 5.6 cm.

(ii) At Q, draw a ray QX making an angle of $45^{\circ}$ and cut off QP = 6 cm.

(iii) At R, draw a ray RY making an angle of $90^{\circ}$ and cut off RS = 2.7 cm.

(iv) Join SP

PQRS is the required quadrilateral.

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Similar questions

Q. Construct a quadrilateral

P Q R S

such that

P Q = 3.5 c m, Q R = 4.5 c m, R S = 4 c m, ∠ Q = 110^{o}

and

∠ R = 80^{o}

PQRS is a quadrilateral in which $P Q = 5 \sqrt{2} c m$ , $Q R = 5 \sqrt{2} c m$ , $R S = 8 c m$ , $S P = 6 c m$ , $∠ P S R = ∠ P Q R = 90^{\circ}$ . Then its area is

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Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ∠Q=45∘ and ∠R=90∘.

Steps of Construction : (i) Draw a line segment QR = 5.6 cm. (ii) At Q, draw a ray QX making an angle of 45∘ and cut off QP = 6 cm. (iii) At R, draw a ray RY making an angle of 90∘ and cut off RS = 2.7 cm. (iv) Join SP PQRS is the required quadrilateral.

Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, $∠ Q = 45^{\circ}$ and $∠ R = 90^{\circ}$ .

Steps of Construction :

(i) Draw a line segment QR = 5.6 cm.

(ii) At Q, draw a ray QX making an angle of $45^{\circ}$ and cut off QP = 6 cm.

(iii) At R, draw a ray RY making an angle of $90^{\circ}$ and cut off RS = 2.7 cm.

(iv) Join SP

PQRS is the required quadrilateral.