Mathematics, 31.07.2019 13:30 saidee1143

The pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula a2 + b2 = c2.

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Answer from: darlasiller

Question with four option

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula, a² + b² = c².If a is a rational number and b is a rational number, why could c be an irrational number?

The square of rational numbers is irrational, and sum of two irrational numbers is irrational.

The product of two rational numbers is rational, and the sum of two rational numbers is irrational.

The left side of the equation will result in a rational number, which is a perfect square.

The left side of the equation will result in a rational number, which could be a non-perfect square.

Answer with Explanation

The Pythagorean theorem states that

Sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

⇒ a² + b² = c²

It has been asked that, a is a rational number and b is a rational number ,then why c is an Irrational number.

Suppose, a=3 ,b=4 , the set of number forming Pythagorean triplet

Then, ⇒ a² + b²

=3²+4²

= 9 +16

=25

= 5²

Here, c=5 is a Rational Number.

Now, take, a=2, b=3,the set of number not forming Pythagorean triplet

a²+b²

=2²+3²

=4 +9

=13

Now, a² + b² = c²

⇒ c²=13

$\rightarrow c^2=13\\\\c=\pm \sqrt{13}$

But side of a triangle can't be negative.

So,Length of Hypotenuse =√13

It totally depends on which two numbers you are choosing, A set of numbers forming Pythagorean Triplet or any other set of numbers.

→ If you choose any other set of numbers which is not a Pythagorean triplet , the Hypotenuse will be an irrational number.

Option D:→ The left side of the equation will result in a rational number, which could be a non-perfect square.

Answer from: Quest

depends on how many days you are talking about

step-by-step explanation:

Answer from: Quest

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 = $6^{2}$

x = 3, y = 216 = $6^{3}$

x = 4, y = 1296 = $6^{4}$

x = 5, y = 7776 = $6^{5}$

so, the geometric series obtained is $6, 6^{2}, 6^{3}, 6^{4}, 6^{5}$ .

thus, the common ratio is given by $\frac{6^{2}}{6}$ = $\frac{36}{6}$ = 6.

hence, the common ratio is 6.

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