Question

Explain how to solve please and thank you =)!

Answer 1

since we know the triangles are similar, that means we can use the corresponding sides of each for proportions

`\cfrac{TU}{QR}=\cfrac{UV}{RS}\implies \cfrac{x+5}{24}=\cfrac{36}{54}\implies \cfrac{x+5}{24}=\cfrac{2}{3}\implies 3x+15=48 \\\\\\ 3x=33\implies x=\cfrac{33}{3}\implies x = 11`

now, the picture is a bit misleading, why did we pick so?

well, one triangle is named QRS, sides QR, RS and SQ

the other triangle is named TUV, sides TU, UV and VT

so you can see which side correspond with the other.