Question

construct triangle PQR, perimeter 14cm angle p=45°, Q=60°.

Answer 1

Hey mate!!!

$<b ><h4>Here is your answer</h4> ; Please refer to the given attachment ;</b >$

Given,
Perimeter is 14cm.
<P = 45.
<Q = 60.

$<b >Steps;</b >$

1) Draw the perimeter XY 14cm.

2) Construct <AXP = 45 and <QYB = 60.

3) Draw the angle bisectors of both <AXP and <QYB, which both meet at R.

4) Now, draw the perpendicular bisectors of RX and RY formed which intersect at P and Q respectively.

5) Join R with P and Q.

6) PQR is the required triangle.

$<b >Verification;</b >$

PR = 4.5Cm, QR = 4Cm, and PQ = 5.5Cm

Adding PR, QR, And PQ, we get,

Perimeter = 14Cm.

Also on measuring,
<P = 45.
<Q = 60.

$<b >Proof</b >$

P lies on the perpendicular bisector of XR.
Thus, XP = PR.
Q lies on the perpendicular bisector of YR.
Thus, QY = QR.

Therefore,
XP + PQ + QY = perimeter.
=> PR + PQ + QR = 14Cm.

Also,
XP = PR

=> <XRP = <PXR

<RPQ = <PXR + <PRX as exterior angle of triangle XRP.

=> <RPQ = 2<PXR

= $2 * \frac{45}{2}$

= 45 degree.

Same as above,

QY = QR

=> <QRY = <QYR

<PQR = <QRY + <QYR as exterior angle of triangle QRY.

=> <PQR = 2<QYR

= $2 * \frac{60}{2}$

= 60 degree.

$<b ><h1 ><marquee ><font color =green >I hope it helps you #need more brainliests marks$

Answer 2

Step-by-step explanation:

okk fine.................