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Pythagoras Theorem

Which of the ...

Question

Which of the following equation satisfies Pythagorean theorem, if a and b are two sides and c is the hypotenuse?

A

c^{2} = a^{2} + b^{2}

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B

a^{2} = b^{2} + c^{2}

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C

b^{2} = a^{2} + c^{2}

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D

c^{2} = a^{2} - b^{2}

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Solution

The correct option is A $c^{2} = a^{2} + b^{2}$
In a right-angled triangle, if c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed by:
$c^{2} = a^{2} + b^{2}$
If the length of both a and b are known, then c can be calculated as
$c = \sqrt{a^{2} + b^{2}}$

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2 s = a + b + c

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} & (s - a)^{2} & (s - a)^{2} (s - b)^{2} & b^{2} & (s - b)^{2} (s - c)^{2} & (s - c)^{2} & c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

a, b

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∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} & {(s - a)}^{2} & {(s - a)}^{2} {(s - b)}^{2} & b^{2} & {(s - b)}^{2} {(s - c)}^{2} & {(s - c)}^{2} & c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

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Q. If sin θ and cos θ are the roots of the equation ax² – bx + c = 0, then a, b and c satisfy the relation
(a) a² + b² + 2ac = 0
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(d) a² – b² – 2ac = 0

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G . P .

(a^{2} + b^{2} + c^{2}) (b^{2} + c^{2} + d^{2}) =

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Pythagoras Theorem

Standard VII Mathematics

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