Question

Construct a quadrilateral PQRS in which PQ=3.5cm, QR=2.5cm, RS=4cm, angleQ=75° and angleR=120°. Also write the steps of construction.

Answer 1

Construction :

Refer to the attachment for the figure.

$\underline{\small\mathfrak{Steps\:of\: Construction\:}}$ -

$\underline{\small\mathfrak{Step\: 1\:}}$ - Draw QR 2 cm.

$\underline{\small\mathfrak{Step\: 2\:}}$ - Construct Angle PQR = 75° at Q.

$\underline{\small\mathfrak{Step\: 3\:}}$ - With Q as the centre and radius = 3.5 cm , cut off QP = 3.5 cm.

$\underline{\small\mathfrak{Step\: 4\:}}$ - Construct Angle QRS = 120° at R.

$\underline{\small\mathfrak{Step\: 5\:}}$ - With R as the centre and radius = 4 cm , cut off RS = 4 cm.

$\underline{\small\mathfrak{Step\: 6\:}}$ - Join PS.

Hence ,

The Quadrilateral so obtained is the required Quadrilateral.

Answer 2

Construct a quadrilateral PQRS, in which PQ=3.5 cm, QR=2.5 cm, RS=4.1 cm,

Solution:-

(i) Draw a line segment QR=2.5 cm.

(ii) At Q, draw a ray QX making an angle of

and cut off QP=3.5 cm.

(iii) At R, draw another ray RY making an angle of

and cut off RS=4.1 cm.

(iv) Join PS.

Then PQRS is the required quadrilateral.