Question

PLEASE HELP! Triangle BCD has the following side lengths: BC = 60, CD = 50

Triangle RST has the following side lengths: RS = 11x-4, ST = 70

What is the value of x? (put just the number in the first box)
What is the length of side RS? (put just the number in the second box)

Answer 1

The value of x is 11 units and the length of side RS = 11x-4 is 117 units.

with measurement BC = 60, CD = 50.

Triangle RST : RS = 11x-4, ST = 70

What is similarity?

Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.

Given:

BC = 60 and CD = 50

RS = 11x - 4 and ST = 70

Now, considering

BC : CD = RS : ST

60 : 50 = 11x - 4 : 70

60/50 = (11x - 4)/70

50 * (11x - 4) = 70 * 60

11x - 4 = 84

11x = 88

x = 11

So, RS = 11x - 4

RS = 11 x 11 - 4

RS = 117

Hence, the value of x is 11 and the length of side RS is 117

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