# Find ac + bd - ad - bc

#### anemone

##### MHB POTW Director
Staff member
Assume that $a, b, c, d$ are positive integers and $\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{3}{4}$, and $$\displaystyle \sqrt{a^2+c^2}-\sqrt{b^2+d^2}=15$$, find $ac+bd-ad-bc$.

Assume that $a, b, c, d$ are positive integers and $\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{3}{4}$, and $$\displaystyle \sqrt{a^2+c^2}-\sqrt{b^2+d^2}=15$$, find $ac+bd-ad-bc$.