Question

Solve for the missing sides of the triangles. The triangles to the right are similar. In the textbox below, solve for y. Remember you can use the button below to input math text for fractions/proportions. Х 36 12 y у 18 972 In the textbox below, solve for x. Remember you can use the button below to input math text for fractions/proportions.

Answer 1

1) What we have here is a case for the Similarity of Triangles. Therefore we can find the missing sides by setting a proportion. Like that

`\begin{gathered} (12)/(y)=(36)/(18+y) \\ 12(18+y)=36y\text{ } \\ \text{Dividing both sides by 12} \\ 18\text{ +y =3y} \\ \text{Subtracting 3y from both sides} \\ -3y+y+18=0 \\ -2y=-18 \\ y=9 \end{gathered}`

1.2) Now let's proceed and find x, based on Similarity we can set another proportion. Considering that y=9.

`\begin{gathered} (12)/(9)=(x)/((9+18+972)) \\ (12)/(9)=(x)/(999) \\ \text{Simplify the first ratio} \\ (4)/(3)=(x)/(999) \\ \text{Cross multiply that} \\ 3x=4\cdot999 \\ 3x=3996 \\ \text{Divide both sides by 3} \\ x=1332 \end{gathered}`

2) So x= 1332 and y =9