In a triangle, ABC, the length of side BC is 10% more than side AB, and length of side AC is 10% less than that of side BC. If the perimeter of triangle ABC is 309 cm, find the length of side AC.
Question
In a triangle, ABC, the length of side BC is 10% more than side AB, and length of side AC is 10% less than that of side BC. If the perimeter of triangle ABC is 309 cm, find the length of side AC.
Solution
Let's denote the length of side AB as x.
According to the problem, BC is 10% more than AB, so BC = 1.1x.
Similarly, AC is 10% less than BC, so AC = 0.9 * BC = 0.9 * 1.1x = 0.99x.
The perimeter of the triangle is the sum of the lengths of all sides, so we have the equation:
x + 1.1x + 0.99x = 309
Solving this equation will give us the value of x, and substituting x into the equation for AC will give us the length of side AC.
Let's solve it:
First, combine like terms on the left side of the equation:
3.09x = 309
Next, divide each side of the equation by 3.09 to solve for x:
x = 309 / 3.09 = 100 cm
Now, substitute x = 100 cm into the equation for AC:
AC = 0.99x = 0.99 * 100 = 99 cm
So, the length of side AC is 99 cm.
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