Question

QT and PMtrianglePQR. If QR = 8 cm, PR 7 cm andQT = 4 cm, what is PM?P=7 cmM=8 cm​

Answer 1

Answer:

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 =  $\dfrac{1}{2} \times \text{Base} \times \text{Height(Altitude)}$

Here, in $\triangle$PQR; Base = PR = 7 cm

Height(Altitude) = QT = 4 cm

So, the area of the triangle PQR =  $\frac{1}{2} \times 7 \times 4$

                                                       =  14 sq cm.

Similarly, the area of the triangle can also be;

Area  =  $\frac{1}{2} \times \text{QR} \times \text{PM}$

Here, QR = Base of triangle PQR = 8 cm

PM = the required altitude

So, Area of triangle  =  $\frac{1}{2} \times 8\times \text{PM}$

              $14 =4 \times \text{PM}$

             PM  =  $\frac{14}{4}$  = 3.5 cm

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