Question

If a/4 = 9/a, then
a²=36
4a = 9a
a + 4 = 9 + a
a - 4 = 9 - a

Answer 1

The answer is a²=36


`(a)/(4) = (9)/(a)`
Multiply both sides of the equation by 4a:

`4a*(a)/(4) =4a* (9)/(a) \\ a*a=4*9 \\ a^(2) =36`

Answer 2

Option A is correct.

The given expression :
`(a)/(4) = (9)/(a)` then;

`a^2 = 36`

Explanation:

Given the expression:
`(a)/(4) = (9)/(a)`

Cross multiplication the given expression following steps are as follow;

• Multiply numerator of the left-hand fraction by the denominator of the right-hand fraction

• Also, Multiply numerator of the right-hand fraction by the denominator of the left-hand fraction.

• then, set the two products equal to each other.

Using cross multiplication, on the given expression;

`(a)/(4) = (9)/(a)`

First multiply the numerator of the left hand fraction(i.e,a ) by the denominator of the right hand fraction (i,e a)

we have;

`(a * a)/(4) = 9`

Simplify:

`(a^2)/(4) =9` [1]

now, multiply numerator of the right-hand fraction( i.e, 9) by the denominator of the left-hand fraction (i.e, 4 ) in [1]

we have;

`a^2 = 9* 4`

Simplify:

`a^2 = 36`

Therefore, the given expression is equal to:
`a^2 = 36`