Question

PQR is a right angled triangle in which PQ = QR. If the hypotenuse of the triangle is 20 cm, then what is the area (in cm2) of the triangle PQR?

Answer 1

$\bold {\huge {Your ~answer :-}}$

$\bf\huge\boxed{100 \: cm^2}$

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EXPLAINATION ➣

Given

→∆PQR is $\green{\texttt{right angled triangle}}$

→The length of $\green{\texttt{hypotenuse}}$= 20 cm

→Length of side PQ = QR = x (let assume)

To find —

The area of given triangle ∆PQR =?

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BY PYTHAGORAS

${PQ}^{2} + {QR}^{2} = {PR}^{2} \\ = > {x}^{2} + {x}^{2} = ( {20})^{2} \\ = > 2 {x}^{2} = 400 \\ = > {x}^{2} = 200 \\ = > x = \sqrt{200} \\ = > x = 10 \sqrt{2}$

Now Area of Right angled triangle

$area = \frac{1}{2} PQ \times QR</p><p> \\ \: \: \: \: \: \: \: = \frac{1}{2} 10 \sqrt{2} \times 10 \sqrt{2} \\ \: \: \: \: \: \: \: \: = 100 \: \: {cm}^{2}$

Verified Answer.

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Answer 2

Answer:

100 cm^2

Step-by-step explanation:

It is given below in the picture