The value of x is 10, given that the two triangles are similar to each other.
What is the relation between the sides of two similar triangles?
The corresponding sides of a pair of similar triangles are in proportion.
This can be shown like this:
If Δ ABC ~ Δ XYZ, that is, triangle ABC is similar to triangle XYZ, we can write that,
AB/XY = BC/YZ = CA/ZX.
How to solve the question?
In the question, we are asked to find the value of x, given that triangle SER is similar to triangle GEF.
∴ Δ SER ~ Δ GEF.
By properties of similar triangles, we can write that:
SE/GE = ΔER/EF = RS/FG,
or, 45/(12x - 3) = 55/143 = RS/FG.
We can use the first two parts of the relation, to form an equation in x, and solve for it.
∴ 45/(12x - 3) = 55/143
or, 12x - 3 = (45 * 143)/55 = 117
or, 12x = 117 + 3 = 120
or, x = 120/12 = 10.
∴ The value of x is 10, given that the two triangles are similar to each other.
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