Mathematics: #9 how do we do it and what is the answer

#9 how do we do it and what is the answer

carethegymnast8954

06.08.2020

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.

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