Question

If 'x' is a very small number compared to 'a', then ratio
of (a+x)2
: a2
is similar to
A) (a+2x) : a
B) (a+x) : a
C) a
2
: a
D) (a+2x) : 2a

Answer 1

Answer:  The correct option is (A) $(a+2x):a.$

Step-by-step explanation:  Given that 'x' is a very small number compared to the number 'a'.

We are to select the ratio that is similar to $(a+x)^2:a^2.$

We have

$(a+x)^2:a^2\\\\\\=\dfrac{(a+x)^2}{a^2}\\\\\\=\dfrac{a^2+2ax+x^2}{{a^2}.}$

Since x is very small compared to a, so x² will be almost negligible compared to a².

Therefore, we can write

$(a+x)^2:a^2\\\\=\dfrac{a^2+2ax+x^2}{a^2}\\\\\\=\dfrac{a^2+2ax}{a^2}\\\\\\=\dfrac{a(a+2x)}{a^2}\\\\\\=\dfrac{a+2x}{a}\\\\\\=(a+2x):a.$

Thus, $(a+x)^2:a^2.$ is similar to $(a+2x):a.$

Option (A) is CORRECT.