Question

I need geometry help

Answer 1

Hi! Answer is x=11 !

Answer 2

x=11

Explanation:

Hi there!

We're given that ΔVUW~ΔSUT (they are similar), and the measures of UV, VW, SU, and ST

UV=5x+11

VW=88

SU=18

ST=24

We need to solve for x

When polygons are congruent, we can create proportional ratios out of their sides; this proportion is known as the ratio of similitude

Since ΔSUT is tilted, it might be kind of difficult to find the corresponding sides to get the ratio of similitude

Instead, we can use the name of the triangles to help us find the corresponding similar parts

ΔVUW and ΔSUT

V corresponds with S

U corresponds with U

that means that UV/SU will give us the ratio of similitude

Which will be
`(5x+11)/(18)`

But we need to find x; we'll need to create another proportion to help us

We have VW and ST, but we need to create the correct proportion first

once again, use the names of the triangles

ΔVUW and ΔSUT

So VW/ST will also get us the ratio of similitude

which is also
`(88)/(24)`, or
`(11)/(3)`

Since both
`(5x+11)/(18)` and
`(11)/(3)` equal the ratio of similitude, we can set them equal to each other

`(5x+11)/(18)`=
`(11)/(3)`

Cross multiply:

3(5x+11)=18(11)

do the distributive property

15x+33=198

subtract 33 from both sides

15x=165

divide both sides by 15

x=11

Hope this helps! :)