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1 year ago

Is 1/4a rational number

Mathematics

2 answers:

neonofarm [45]1 year ago

7 0

The number 1 /4 is a fraction, and fractions are ratios, and ratios are ratio-nal numbers!

Explanation:

Every fraction is comparing one number to another. So, for example, the number 2 /5 is comparing the number 2 with the number 5. In this case, the fraction is saying that 2 is the fractional part and 5 is the whole part. So if a pizza was cut into 5 equal slices, and I ate 2 of those slices, I would have eaten

2 /5 of the pizza.

The ratio is a different way of saying exactly the same thing. Instead of writing 2/5, we could write 2:5, which is a ratio comparing 2 to 5. Therefore, every rational number is a number that can be expressed as a quotient a/b of two integers. The integer a is called the numerator, and the integer b is called the denominator and cannot be zero (0).

hope it helps!

12345 [234]1 year ago

5 0

Yes 1/4 is a rational number

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Given: ΔABC is equilateral and AB = a

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Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.

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Now in ΔAMB , By using Pythagoras theorem

$AB^{2}=AM^{2}+MB^{2}\\AM^{2}=AB^{2}-MB^{2}\\AM^{2}=a^{2}-(\frac{a}{2})^{2}\\AM=\frac{\sqrt{3}\cdot a}{2}$

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$sin\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\sin\thinspace 30^{o}=\frac{\text{MB}}{\text{PB}}\\\\PB=\frac{\text{MB}}{\text{sin 30}}\\\\PB=\frac{\frac{a}{2}}{\frac{1}{2}}\implies PB = a\\\\tan\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Base}}\\\\tan\thinspace 30^{o}=\frac{\text{MB}}{\text{PM}}\\\\PM=\frac{\text{MB}}{\text{tan 30}}\\\\PM=\frac{\frac{a}{2}}{\frac{1}{\sqrt3}}\implies PM=b= \frac{\sqrt{3}\cdot a}{2}$

Perimeter of ABM = AB + PB + PM + AM

$\text{Perimeter = }a+a+b+ \frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a + \frac{\sqrt{3}\cdot a}{2} +\frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a +\sqrt{3}\cdot a\\\\=(2+\sqrt3})\cdot a$

Hence, Perimeter of ΔABP = (2 + √3)·a units

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1 year ago

Is 1/4a rational number​

Is 1/4a rational number