Question

If QRS ~ TUV, then find the value of x

Answer 1

x=11

Step-by-step explanation:

If triangles QRS and TUV are similar, then the ratio of the corresponding sides are:

`(QR)/(TU)=(QS)/(TV)=(RS)/(UV)`

Substituting the given lengths:

`\begin{gathered} (24)/(x+5)=(QS)/(TV)=(54)/(36) \\ \implies(24)/(x+5)=(54)/(36) \end{gathered}`

We solve the equation above for x:

`\begin{gathered} 54(x+5)=24*36 \\ x+5=(24*36)/(54) \\ x+5=16 \\ x=16-5 \\ x=11 \end{gathered}`

The value of x is 11.