The expression $15 x + 11$ represents the perimeter of the trapezoid. What is the length of the fourth side? Explain your reasoning.

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Solution

Hint: Perimeter of the trapezoid = sum of all four sides
Step 1: We have given:
Perimeter of the trapezoid $= 15 x + 11$
We know that perimeter of the trapezoid = sum of all four sides
$= 2 x + 3 + 3 x + 4 + 4 x - 1 + f o u r t h s i d e l e n g t h$
Equating both the perimeters:
$2 x + 3 + 3 x + 4 + 4 x - 1 + f o u r t h s i d e l e n g t h = 15 x + 11 9 x + 7 - 1 + f o u r t h s i d e l e n g t h = 15 x + 11 9 x + 6 + f o u r t h s i d e l e n g t h = 15 x + 11 f o u r t h s i d e l e n g t h = (15 x + 11) - (9 x + 6) = 15 x + 11 - 9 x - 6$
The length of the fourth side $= 6 x + 5$
Final Answer: The length of the fourth side $= 6 x + 5$

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The expression 15x+11represents the perimeter of the trapezoid. What is the length of the fourth side? Explain your reasoning.

The expression $15 x + 11$ represents the perimeter of the trapezoid. What is the length of the fourth side? Explain your reasoning.