Answer:
x = 11
Step-by-step explanation:
From the diagram, we can see that there is a small triangle embedded inside a larger triangle and that both triangles are similar to one another. We are also given values to two sides of the triangles.
Because the triangles are similar, we know that the ratio of the length of their sides are equal. i.e.
equating the ratios of sides for small triangle / large triangle:
6 /(6+48) = 5 / [ 5 + (3x+7) ]
6 /54 = 5 / ( 5 + 3x+7 )
6 /54 = 5 / ( 12 + 3x ) (multiplying both sides by 54 and (12+3x) )
6 (12+3x) = 5(54)
72 + 18x = 270 (subtract 72 from both sides)
18x = 270 - 72
18x = 198 (divide both sides by 18)
x = 198 / 18
x = 11
