Question

I need help figuring out the measures of the missing sides

Answer 1

Given:

• c = 20

,

• h = 15

,

• j = 12

,

• k = 16

Let's find the measures of the mssing sides if triangle ABC is similar to triangle JKH.

Here, the missing sides are:

Side a and Side b

Since both triangles are similar, the corresponding sides will be proportional.

To solve for the length of side a, apply the proportionality equation:

`(c)/(h)=(a)/(j)`

Plug in values and solve for a:

`\begin{gathered} (20)/(15)=(a)/(12) \\ \\ \text{ Cross multiply:} \\ 15a=20*12 \\ \\ 15a=240 \\ \text{ } \\ \text{ Divide both sides by 15:} \\ (15a)/(15)=(240)/(15) \\ \\ a=16 \end{gathered}`

Thereofore, the length of side a = 16

To solve for the length of side b, apply the equation:

`(c)/(h)=(b)/(k)`

Plug in the values for the variables and solve for b:

`\begin{gathered} (20)/(15)=(b)/(16) \\ \\ 15b=20*16 \\ \\ 15b=320 \\ \\ b=(320)/(15) \\ \\ b=21.3 \end{gathered}`

The length of b is 21.3

ANSWER:

• a = 16

,

• b = 21.3