Question

What can you conclude from the given information.

Apply the means-extremes property to $\frac{a}{b}=\frac{c}{d}$and also to$\frac{a}{c}=\frac{b}{d}$

Short answer

Both proportion gives the same equation.

Step-by-step solution

Step 1. Given information.

The given proportions are,

$\frac{a}{b}=\frac{c}{d}and\frac{a}{c}=\frac{b}{d}$.

It is given, $\frac{a}{b}=\frac{c}{d}and\frac{a}{c}=\frac{b}{d}$

For the proportion$a:b::c:d$

i.e,$\frac{a}{b}=\frac{c}{d}$

$aandd$are called extreme and$bandc$ are called means.

Step 2. Now, from the means-extreme property.

Product of means and product of extremes are equal.

Step 3. for the proportionab=cd  .

Means-extremes property gives,$ad=bc$

Similarly,

Step 4. For the proportionac=bd  .

Means-extremes property gives$ad=bc$,

Therefore, both proportion gives the same equation.