Question

Swer choice that best completes the statement or answers the question. GEOMETRY The expressions (5x)/(2),(20)/(x+4), and (10)/(x-4) represent the lengths of the sides of a triangle. Write a simplified

Answer 1

The expressions (5x)/(2), (20)/(x+4), and (10)/(x-4) represent the lengths of the sides of a triangle. To write a simplified ratio, we find a common denominator and simplify each expression.

Step-by-step explanation:

The expression (5x)/(2), (20)/(x+4), and (10)/(x-4) represent the lengths of the sides of a triangle. To find a simplified ratio, we can start by finding a common denominator for the three expressions. The common denominator for (2), (x+4), and (x-4) is 2(x+4)(x-4). We can then simplify each expression by multiplying the numerator and denominator by the common denominator:

(5x)/(2) = (5x * 2(x+4)(x-4))/(2 * 2(x+4)(x-4)) = (10x(x+4)(x-4))/(4(x+4)(x-4))

(20)/(x+4) = (20 * 2(x+4)(x-4))/(2(x+4)(x-4)) = (40(x+4)(x-4))/(2(x+4)(x-4)) = (20(x+4)(x-4))/(x+4)(x-4)

(10)/(x-4) = (10 * 2(x+4)(x-4))/(2(x+4)(x-4)) = (20(x+4)(x-4))/(2(x+4)(x-4)) = (10(x+4)(x-4))/(x+4)(x-4)

Now we can write the simplified ratio: (10x(x+4)(x-4))/(4(x+4)(x-4)) : (20(x+4)(x-4))/(x+4)(x-4) : (10(x+4)(x-4))/(x+4)(x-4)