Question

সৃজনশীল প্রঞ্জ- ০১
PQR একটি সমবাহু ত্রিভুজ এবং PS, Q R এর উপর লম্ব।
ক. 20 = 3CM হলে, A ) R এর ক্ষেত্রফল নির্ণয় কর।
* প্রমাণ কর যে, P) + PR> 21PS
গ প্রমাণ কর যে, 4192 = 3/P7R?​

Answer 1

Answer:

3CM হলে, A ) R এর ক্ষেত্রফল নির্ণয়

Answer 2

Answer:

The coordinates of P are $(2 \sqrt{ } 3,0)$.

Step-by-step explanation:

Step 1: Given PQR is an equilateral triangle in which Q(0,2) and R(0,−2).

Let (x,0) be the coordinates of P. [∵P lies on x axis. So y-coordinate is zero.]

PQ=PR=QR=2+2=4

OQ=2 [from figure]

Step 2:The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

In POQ,

$\begin{aligned}& \left.\mathrm{PQ}^2=\mathrm{OP}^2+\mathrm{OQ}^2 \text { [Pythagoras theorem }\right] \\& 4^2=\mathrm{OP}^2+2^2 \\& \mathrm{OP}^2=4^2-2^2 \\& \mathrm{OP}^2=16-4 \\& \mathrm{OP}^2=12 \\& \mathrm{OP}=\sqrt{ }(4 \times 3)=2 \sqrt{3}\end{aligned}$

Hence the coordinates of P are $(2 \sqrt{ } 3,0)$.

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