Question

If △HBN∼△LYR, find the value of x. ​

Answer 1

`\huge\boxed{\sf x = 13}`

Explanation:

For similar triangles, sides of the triangles are proportional.

So,

`\displaystyle (LY)/(HB) =(LR)/(HN) \\\\(21)/(28) =(x + 11)/(3x-7) \\\\Cross\ multiply\\\\21(3x-7)=28(x+11)\\\\63x-147=28x+308\\\\Subtract\ 28x\ to\ both\ sides\\\\63x-28x-147=308\\\\35x-147=308\\\\Add \ 147 \ to \ both \ sides\\\\35x = 308+147\\\\35x = 455\\\\Divide \ 35 \ to \ both \ sides\\\\x = 455/35\\\\x = 13\\\\`

`\rule[225]{225}{2}`