triangle STU is an equilateral triangle. If ST is one less than twice x, SU is 37 less than five times x, and TU is 11 more than x, find x and the measure of each.
Accepted Solution
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Answer:The value of x = 12 and the measure of each side is 23 units.Step-by-step explanation:Given: STU is an equilateral triangle.ST = 2x -1SU = 5x - 37TU = x + 11Now, as Δ STU is an equilateral triangle, hence all the sides of the triangle are equal.⇒ ST = SU = TUor, 2x -1 = 5x - 37 = x + 11Considering : 2x -1 = 5x - 37 , we get-1 + 37 = 5x - 2xor 3x = 36or, x = 12Considering : 5x - 37 = x + 11 , we get5x -x = 11 + 37or, 4x = 48 or, x = 12Considering : x + 11 = 2x -1or, 2x - 1 = x + 11or, x = 12hence, in all the cases value of x = 12ST = 2x -1 = 2(12) -1 = 23 unitsSU = 5x - 37= 5(12) -1 = 23 unitsTU = x + 11 = 12 = 11 = 23 units