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The value of the variable x for the length of the similar to triangle ∆RST is equal to 17.5 The correct option is C.
Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
10/(10 + x) = 8/(8 + 14)
10/(10 + x) = 8/22
8(10 + x) = 22 × 10 {cross multiplication}
80 + 8x = 220
8x = 220 - 80 {collect like terms}
8x = 140
x = 140/8 {divide through by 8}
x = 17.5
Therefore, the value of the variable x for the length of the similar to triangle ∆RST is equal to 17.5
Read more about similar triangles here:https://brainly.com/question/14285697
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