Hello from MrBillDoesMath
Answer:
x = 6
Discussion:
We are told the triangles are similar so corresponding parts have equal ratios
. In our case this becomes
(5x-2)/7x = (3x+2)/5x
and we need to solve for "x". Multiply both sides by x
(5x-2)/7x*x = (3x+2)/5x*x =>
(5x -2)/7 = (3x+2)/5 ( as x/x = 1)
Multiply both sides by 35 ( = 7 * 5)
(5x-2)/ 7 * (7*5) = (3x +2 )/ 5 * (7*5) =>
(5x-2) * 5 = (3x +2) * 7 =>
25x -10 = 21x + 14 => (subtract 21x from both sides)
(25x - 21x) - 10 = 14 => (simplify)
4x - 10 = 14 => (add 10 to both sides)
4x = 14 + 10 =>
4x = 24 =>
x = 6
Thank you,
Mr. B
