Answer :
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If a straight line connecting two sides of a triangle is parallel to its third side then the straight line divides these sides proportionally.
If the lengths of the segments are listed in an corresponding order, then it implies that you have this proportion:
x + 8/x = x + 1/x +13
Contradiction. This equation has no solutions in real positive numbers. It means that the lengths are listed in the inverse order. Then the proportion is
x + 8/x = x +13/ x+1
If a straight line connecting two sides of a triangle is parallel to its third side then the straight line divides these sides proportionally.
If the lengths of the segments are listed in an corresponding order, then it implies that you have this proportion:
x + 8/x = x + 1/x +13
Contradiction. This equation has no solutions in real positive numbers. It means that the lengths are listed in the inverse order. Then the proportion is
x + 8/x = x +13/ x+1
Answer:
AC = 18.
Step-by-step explanation:
The problem is about proportions, because we have two parallels line being intercepted by two transversal. So, the proportion would be:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}[/tex]
Solving for [tex]x[/tex]:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}\\(x+1)(x+8)=x(x+13)\\x^{2} +8x+x+8=x^{2} +13x\\9x+8=13x\\8=13x-9x\\4x=8\\x=\frac{8}{4}=2[/tex]
Now, to find the length of AC, we just have to use the value found and replace it in the proper expression:
[tex]AC=x+13+x+1=2x+14=2(2)+14=4+14=18[/tex]
Therefore, the length of AC is 18.