Question

I did 3 over 7 then 8 over x. I'm getting decimals. ‍♀️

Answer 1

The length of side b is 9.

Explanation:

Triangles are similar if they have the same shape, but can be different sizes.

When two figures are similar, the ratios of the lengths of their corresponding sides are equal.

If you know that two objects are similar, you can use proportions and cross products to find the length of an unknown side. We know that the triangle
`ABC` is similar to the triangle
`XYZ`. Therefore the following relation must be true:

`(AB)/(AC) =(XY)/(XZ)`

We know that side
`AB` is equal to 8, side
`AC` is equal to b, side
`XY` is equal to
`2(2)/(3)`, and side
`XZ` is equal to 3.

Substituting these values into the above relation and solving for b we get that:

`(8)/(b) =(2(2)/(3) )/(3)\\\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2(2)/(3)=(8)/(3)\\\\(8)/(b)=((8)/(3))/(3)\\\\8\cdot \:3=b(8)/(3)\\\\24=b(8)/(3)\\\\8b=72\\\\b=9`