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 = [tex]\dfrac{1}{2} \times \text{Base} \times \text{Height(Altitude)}[/tex]
Here, in [tex]\triangle[/tex]PQR; Base = PR = 7 cm
Height(Altitude) = QT = 4 cm
So, the area of the triangle PQR = [tex]\frac{1}{2} \times 7 \times 4[/tex]
= 14 sq cm.
Similarly, the area of the triangle can also be;
Area = [tex]\frac{1}{2} \times \text{QR} \times \text{PM}[/tex]
Here, QR = Base of triangle PQR = 8 cm
PM = the required altitude
So, Area of triangle = [tex]\frac{1}{2} \times 8\times \text{PM}[/tex]
[tex]14 =4 \times \text{PM}[/tex]
PM = [tex]\frac{14}{4}[/tex] = 3.5 cm
Hence, the length of the altitude PM is 3.5 cm.
