Answer:
yes; x=7
Step-by-step explanation:
When two corresponding angles are congruent, all angles are congruent, so the triangles are similar. The sides of the triangle on the right are 30/25 = 6/5 times the length of the sides of the left triangle, so side MP will be 6/5 times the length of JL, or (6/5)·20 = 24.
Then the expression for that length lets us find the value of x:
24 = 4x -4
6 = x -1 . . . . . divide by 4
7 = x . . . . . . . add 1
Solve for x over the real numbers:
-5 + 1/5 + 3/x = 9/20
-5 + 1/5 + 3/x = 3/x - 24/5:
3/x - 24/5 = 9/20
Bring 3/x - 24/5 together using the common denominator 5 x:
-(3 (8 x - 5))/(5 x) = 9/20
Cross multiply:
-60 (8 x - 5) = 45 x
Expand out terms of the left hand side:
300 - 480 x = 45 x
Subtract 45 x + 300 from both sides:
-525 x = -300
Divide both sides by -525:
Answer: x = 4/7
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