A rectangle's length is 3 times its width. If the area is 75 square meters, what

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Question: A rectangle\'s length is 3 times its width. If the area is 75 square meters, what is the length?

Options:

Correct Answer: 15 meters

Solution:

Let width = x, then length = 3x. Area = length × width = 3x * x = 3x² = 75. Thus, x² = 25, x = 5, and length = 15 meters.

A rectangle's length is 3 times its width. If the area is 75 square meters, what is the length?

A rectangle's length is 3 times its width. If the area is 75 square meters, what is the length?

Step 1: Let the width of the rectangle be represented by 'x'.
Step 2: Since the length is 3 times the width, we can express the length as '3x'.
Step 3: The formula for the area of a rectangle is 'Area = length × width'.
Step 4: Substitute the expressions for length and width into the area formula: Area = 3x × x.
Step 5: This simplifies to Area = 3x².
Step 6: We know the area is 75 square meters, so we set up the equation: 3x² = 75.
Step 7: To solve for x², divide both sides of the equation by 3: x² = 75 / 3.
Step 8: This simplifies to x² = 25.
Step 9: To find x, take the square root of both sides: x = √25.
Step 10: This gives us x = 5 meters, which is the width.
Step 11: Now, to find the length, multiply the width by 3: length = 3 × 5.
Step 12: This gives us the length = 15 meters.

Area of a Rectangle – Understanding the formula for the area of a rectangle (Area = length × width) and how to manipulate it to find unknown dimensions.
Algebraic Manipulation – Using algebra to express relationships between variables and solve for unknowns.
Proportional Relationships – Recognizing and applying proportional relationships between length and width in geometric figures.