Construct a quadrilateral PQRS in which PQ = 5 cm,QR = 7.5 cm, RS = PS = 6.5 cm, PR = 10 cm. Measure the diagonal QS.

Hint: In such types of problems we must first make a rough sketch of the diagram from the given data. After making a rough sketch we have to proceed in the sequence that we went through during making the rough sketch.

Complete step-by-step answer:


a. Firstly, we draw a line PQ of length 5cm.
b. Then with a centre Q, keeping the needle of geometric compass at Q, we have to mark an arc QR = 7.5cm.
c. Again with a centre P, keeping the needle of geometric compass at P, we have to again mark an arc at PR = 10cm.
d. We will join QR and PR. After joining the Point P & R and Q & R we get a Triangle Named PQR with P, Q, R being 3 corners.
e. Now with the centre P, keeping the needle of geometric compass at P,we have to mark an arc PS = 6.5cm.
f. Again with a centre R, keeping the needle of geometric compass at R, again we have to mark an arc at RS = 6.5cm.
g. Again we join PS and RS. and finally we get our quadrilateral PQRS.
h. After we complete our Quadrilateral PQRS we have to measure QS which come out to be 7.9 cm
i. Hence our answer is length of diagonal QS is 7.9 cm

Note: - While solving such types of problems we must always keep in mind that there will be differences between the rough sketch and the final diagram. So we must keep in mind the original data given and proceed as per the rough sketch sequence.