Question

triangle PQR is isosceles with PQ = PR = 7.5 cm and QR = 9cm. the height PS from P to QR, is 6cm. find the area of triangle PQR. what will be the height from R to PQ i.e RT ?
please answer fast...............

Answer 1

the area of isosceles triangle =b/4
√4b^2-a^2
by puting value the answer is 27 second part u can do by Pythagoras theorem

Answer 2

The area of triangle PQR is 27 square centimeter. The height of RT is 7.2 cm

Solution:

In the given isosceles triangle PQR , PQ = PR = 7.5cm and QR = 9cm, PS = 6cm

The diagram is attached below

The area of triangle is given as:

$\text { Area of Triangle }=\frac{1}{2} \times base \times height$

Here base = QR and height = PS

$\begin{array}{l}{\text { Area of Triangle }=\frac{1}{2} \times Q R \times P S} \\\\ {\text { Area of Triangle }=\frac{1}{2} \times 9 \times 6=27}\end{array}$

Thus the area of triangle PQR is 27 square centimeter

To find height from R to PQ i.e RT:

$\text { Area of Triangle } \mathrm{PQR}=\frac{1}{2} \times P Q \times R T$

$\begin{array}{l}{27=\frac{1}{2} \times 7.5 \times R T} \\\\ {\frac{27 \times 2}{7.5}=\mathrm{RT}} \\\\ {\mathrm{RT}=7.2}\end{array}$

Thus the height of RT is 7.2 cm

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