Question

What are the values of x and y? Type the correct answer in each box. Use numerals instead of words.

Answer 1

From the given figure,

`\Delta PQR\text{ is similar to }\Delta STU`

When two triangles are similar then ratio of their corresponding sides are similar.

`(PQ)/(ST)=(QR)/(TU)=(PR)/(SU)`

Substituting the values in the above equation,

`(8)/(16)=\frac{10}{x\text{ + 3}}=(5y-1)/(28)`

Calculating the value of x ,

`\begin{gathered} (8)/(16)=\text{ }(10)/(x+3) \\ 8(x+3)=10*16 \\ 8x+24=160 \end{gathered}`

Rearranging the like terms o both the sides ,

`\begin{gathered} 8x\text{ = 160 - 24} \\ 8x\text{ = 136} \\ x\text{ = }(136)/(8) \\ x\text{ = 17} \end{gathered}`

Calculating the value of y,

`\begin{gathered} (8)/(16)\text{ = }(5y-1)/(28) \\ 8\text{ }*\text{ 28 = }16*\text{ (5y-1)} \\ 224\text{ = 80y - 16} \\ \end{gathered}`

Rearranging the like terms on both the sides ,

`\begin{gathered} 224\text{ + 16 = 80y} \\ 80y\text{ = 240} \\ y\text{ = }(240)/(80) \\ y\text{ = 3} \end{gathered}`

Thus the required values of x and y are ,

`\begin{gathered} x\text{ = 17} \\ y\text{ = 3} \end{gathered}`