Question

Pleasee help mee ;w;

Answer 1

The ratio of sides remains same

`\\ \sf\longmapsto (PQ)/(QS)=(RQ)/(RS)`

`\\ \sf\longmapsto (21)/(15)=(5x-16)/(3x-4)`

`\\ \sf\longmapsto (7)/(5)=(5x-16)/(3x-4)`

`\\ \sf\longmapsto 7(3x-4)=5(5x-16)`

`\\ \sf\longmapsto 21x-28=25x-80`

`\\ \sf\longmapsto 80-28=25x-21x`

`\\ \sf\longmapsto 4x=52`

`\\ \sf\longmapsto x=13`

Answer 2

• x = 13

Explanation:

It is assumed PQS and RQS are similar triangles.

The ratio of corresponding sides is equal:

• PS/RS = PQ/RQ

Substitute side lengths and solve for x:

• 15/(3x - 4) = 21/(5x - 16)
• 15(5x - 16) = 21(3x - 4)
• 5(5x - 16) = 7(3x - 4)
• 25x - 80 = 21x - 28
• 25x - 21x = 80 - 28
• 4x = 52
• x = 52/4
• x = 13