By applying the basic proportionality theorem to this triangle, the value of x is 7 cm.
In Mathematics and Euclidean Geometry, the basic proportionality theorem states that when any of the two sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two sides that are intersected would be divided proportionally and in constant ratio.
By applying the basic proportionality theorem to this triangle, we have the following proportional side lengths:
5/40 = 3/(2x + 10)
5(2x + 10) = 120
10x + 50 = 120
10x = 120 - 50
10x = 70
x = 70/10
x = 7 cm.