Question

Why is ac smaller than ad if they both look very close

Answer 1

Let's begin by listing out the information given to us:

We start out by observing that Triangles MKR & ACD are similar or proportional

`\begin{gathered} MK=21;AC=\text{?} \\ MR=24;AD=28(4)/(5) \\ KR=CD=\text{?} \end{gathered}`

We will solve for the missing side by using the similar triangle theorem. This is shown below:~

`\begin{gathered} \Delta MKR\approx\Delta ACD \\ (MK)/(AC)=(MR)/(AD) \\ (21)/(AC)=(24)/(28(4)/(5)) \\ \text{Cross multiply, we have:} \\ 24\cdot AC=28(4)/(5)\cdot21 \\ AC=(28(4)/(5)\cdot21)/(24)=25(1)/(5) \\ AC=25(1)/(5) \end{gathered}`