23. Construct a APQR, in which QR=6.5cm,2Q=60° and PR-PQ=1.5 cm.
24.Express y in terms of x from the equation 3x+5y=12 and check whether (-1,3) is it solution or not.
25. If +-1, find x-y?
26. Internal and external diameters of a hollow hemispherical vessel are 24 cm and 25 cm, respectively. T
Answers
Answer:
23.Given, in APQR,
QR = 6.5 cm, ZQ = 60° and =
PR - PQ =1.5 cm
Steps of construction
(i)Draw the base, QR = 6.5 cm
At point Q, draw a ray QX making an ZXQR = 60°.
Here, PR - PQ = 1.5 cm
PR > PQ
i.e. the side containing the base angle 0 is less than third side, so it is the case II.
(ii)Cut line segment OS equal to PR-PQ, i.e. OS =1.5 cm from the ray OX extended on opposite side of base QR.
(iii)Join SR and draw its perpendicular bisector ray AB, which intersects SR at M
(iv)Let P be the intersection point of SX and perpendicular bisector AB. Then, join PR.Thus, APQR is the required triangle.
Justification
Base QR and Q are drawn as given.
Since, AB is the perpendicular bisector of
SR and P lies on it.
.: PS = PR
Now, QS = PS - PQ
=> QS= PR-PQ
Thus, construction justified.
