Question

Guys please help me thank you!

Answer 1

x = 16 2/3

Explanation:

The two triangles in the picture are similar, which means that the corresponding side lengths on each of them are proportional - the ratios between them are equal to each other.

On the larger triangle, let's pick the pair of lengths 25 and 39. The corresponding pair on the triangle has the lengths x and 26. Similarity then tells us that the ratios, 25/39 and x/26, are equivalent. All that's left to do now is set up an equation and solve for x:

`(25)/(39)=(x)/(26)`

multiplying both sides of the equation by 26 gives us

`26\left((25)/(39)\right)=x`

We can do a little reduction here: 26 and 39 have a common factor of 13, and since 26 = 13 x 2 and 39 = 13 x 3, the expression on the left reduces to

`2\left((25)/(3)\right)=x`

We can rewrite 25/3 as the mixed number 8 1/3, making our equation

`2\left(8(1)/(3)\right) =x`

So finally, we have
`x=16(2)/(3)`