Question

In the figure, ΔRED is similar to ΔRSF. What is the value of x, the length of side RS?
    
  A. 10.5
  B. 14
  C. 4.6
  D. 17

Answer 1

the answer is 14 , because  21-12= 9 then 12/9=8/x. 12x=72, divide by 12, then you will get 6, which is the length of the missing side. Then you add 8+6 to find the length of RS and it is 14.

Answer 2

The length of side RS and the value of x is 14.

Concept:

• The fundamental concept used in the given question is the Basic Proportionality Theorem.
• It states that if two triangles are similar, the ratio of their corresponding sides will be equal.

How to solve the given question?

• As ΔRED is similar to ΔRSF, As per the Basic Proportionality theorem,
  
  $\frac{RE}{ES} = \frac{RD}{RF}$
  ∴ $\frac{8}{x} = \frac{12}{21}$
  ∴$x = \frac{21}{12} \ 8$
  ∴ x  = 14

The length of side RS and the value of x is 14.

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