QT and PM
trianglePQR. If QR = 8 cm, PR 7 cm and
QT = 4 cm, what is PM?
P=7 cm
M=8 cm

The length of the altitude PM is 3.5 cm.

Step-by-step explanation:

We are given that QT and PM  are the altitudes of the triangle PQR. Also, QR = 8 cm, PR = 7 cm and  QT = 4 cm.

We have to find the length of the altitude PM.

As we know that the area of the triangle is given by;

Area of triangle =  

Here, in PQR; Base = PR = 7 cm

Height(Altitude) = QT = 4 cm

So, the area of the triangle PQR =  

                                                       =  14 sq cm.

Similarly, the area of the triangle can also be;

Area  =  

Here, QR = Base of triangle PQR = 8 cm

PM = the required altitude

So, Area of triangle  =  

             PM  =    = 3.5 cm

Hence, the length of the altitude PM is 3.5 cm.

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option