Part I: Evaluating the value of "a"
Given equation:
[tex]\cfrac{a}{4} = \cfrac{9}{a}[/tex]
To simplify the equation, we need to use cross multiplication.
[tex]\text{Cross multiplication:}\ \huge\text{[(}\dfrac{a}{b} = \dfrac{c}{d} \huge\text{)} \implies \huge\text{(}a \times d = b \times c\huge\text{)} \implies ad = bd \text{]}[/tex]
After using cross multiplication, we obtain;
[tex]\implies a \times a= 9 \times 4[/tex]
[tex]\implies a^{2} =36[/tex]
Taking a square root on both sides of the equation:
[tex]\implies \sqrt{a^{2}} =\sqrt{36}[/tex]
[tex]\implies a =6[/tex]
Part II: Determining the correct option:
This can be done by substituting the value of "a" in all the options. The option, which is true, is correct.
Verifying Option A:
Given equation:
Substitute the value of "a" into the equation
Simplify the left-hand-side of the equation:
- ⇒ (6)² = 36
- ⇒ (6)(6) = 36
- ⇒ 36 = 36 (True)
Verifying Option B:
Given equation:
Substitute the value of "a" into the equation
Simplify both sides of the equation:
- ⇒ 4(6) = 9(6)
- ⇒ 24 = 54 (False)
Verifying Option C:
Given equation:
Substitute the value of "a" into the equation
- ⇒ a + 4 = 9 + a
- ⇒ (6) + 4 = 9 + (6)
Simplify both sides of the equation:
- ⇒ (6) + 4 = 9 + (6)
- ⇒ 10 = 15 (False)
Verifying Option D:
Given equation:
Substitute the value of "a" into the equation:
- ⇒ a - 4 = 9 - a
- ⇒ (6) - 4 = 9 - (6)
Simplify both sides of the equation:
- ⇒ (6) - 4 = 9 - (6)
- ⇒ 2 = 3 (False)
Therefore, Option A is correct.
