Question

construct a triangle pqr in which qr=8cm,q=45degree and pq-pr=3.5cm

Answer 1

Given, inv ΔPQR, QR = 3 cm, ∠PQR = 45°
and QP – PR = 2 cm
Since, C lies on the perpendicular bisector RS of AY.
To construct ΔPQR, use the following steps.
1.Draw the base QR of length 3 cm.
2.Make an angle XQR = 45° at point Q of base QR.
3.Cut the line segment QS =QP- PR = 2 cm from the ray QX.



4.Join SR and draw the perpendicular bisector of SR say AB.
5.Let bisector AB intersect QX at P. Join PR Thus, ΔPQR is the required triangle.
Justification
Base QR and ∠PQR are drawn as given.
Since, the point P lies on the perpendicular bisector of SR.
PS = PR
Now, QS = PQ – PS
= PQ -PR
Thus, our construction is justified.

Done

Answer 2

$steps \: of \: construction$
1)We draw a line segment QR=8cm.
2)Using ruler and compass we construct angle(XQR)=45°.
3)From QX, we cut off QY=3.5cm and YR is joined.
4)We construct the perpendicular bisector EF of YR which when produced to cut QX at the point P and PR is joined.
Thus,PQR is the required triangle.