If PQR is an equilateral triangle and PX ⊥ QR, find the value of PX^2.

In the given figure, PQR is an equilateral triangle and OSPT is a square. If OT=2sqrt2 units find the equation of lines OT, OS, SP, QR, PR, and PQ .

The base PQ of two equilateral triangles PQR and PQR’ with side 2a lies along y-axis such that the mid-point of PQ is at the origin. Find the coordinates of the vertices R and R’ of the triangles.

The vertex P of an equilateral triangle trianglePQR is at (2,3) and the equation of the opposite side QR is given by x+y=2 . Find the possible equations of the side PQ.

The base QR of an equilateral triangle PQR lies on X-axis. The co-ordinates of the point Q are (-4,0) and origin is the mid-point of the base. Find the co-ordinates of the points P and R.

Delta PQR is right angled isosceles triangle, right angled at R. Find value of sin P.

In the figure, given below, PQR is a right angled triangle right angled at Q. XY is parallel to QR, PQ = 6 cm, PY = 4 cm and PX : XQ = 1:2. Calculate the lengths of PR and QR.

If p-15=0 and 2x^(2)+px+25=0 , find the values of x.

PQR is a triangle right angled at P. If PQ=10cm and PR=24cm, find QR

In triangle PQR. angleQ is a right angle, QR=24, and PR=26. Triangle YXZ is similar to triangle PQR, where vertices X, Y, and Z correspond to vertices P, Q, and R, respectively, and each side of triangle XYZ is (1)/(2) the length of the corresponding side of triangle PQR. What is the value of sin Z?

If x=1(1)/(2) is a solution of the equation 2x^(2)+px-6=0 , find the value of 'p'.