Calculate Rectangle Perimeter: Area 105 with Width 15 and Height 7

Q: Why don't I need to use the area of 105 to find the perimeter?

The area (105) is extra information in this problem! Since you already know both dimensions (width = 15, height = 7), you can calculate perimeter directly without using the area.

Q: How do I remember which formula to use for perimeter?

Think of perimeter as the fence around a garden. You need to add up all the sides to know how much fencing to buy: length + width + length + width.

Q: Can I use P = 2l + 2w instead of P = 2(l + w)?

Yes, both formulas work perfectly! P = 2l + 2w = 2(15) + 2(7) = 30 + 14 = 44. Use whichever formula feels easier for you.

Q: How can I check if my perimeter answer makes sense?

Your perimeter should always be larger than any single side. Since our longest side is 15, and our perimeter is 44, this makes sense because 44 > 15.

Rectangle Perimeter with Given Dimensions

The area of a rectangle is equal to 105.

Calculate its perimeter using the data in the figure below.

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Understand the problem

The area of a rectangle is equal to 105.

Calculate its perimeter using the data in the figure below.

Step-by-step solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=15$

$AC=BD=7$

Now let's calculate all the sides together to find the perimeter of the rectangle:

$7+15+7+15=14+30=44$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter = 2 × (length + width)
Calculation: P = 2 × (15 + 7) = 2 × 22 = 44
Verify: Count all four sides: 15 + 7 + 15 + 7 = 44 ✓

Common Mistakes

Avoid these frequent errors

Using area formula instead of perimeter
Don't multiply length × width to find perimeter = 105! That gives you area, not the distance around the rectangle. Always add all four sides together for perimeter.

Practice Quiz

Test your knowledge with interactive questions

Given the following rectangle:

Find the area of the rectangle.

FAQ

Everything you need to know about this question

Why don't I need to use the area of 105 to find the perimeter?

The area (105) is extra information in this problem! Since you already know both dimensions (width = 15, height = 7), you can calculate perimeter directly without using the area.

How do I remember which formula to use for perimeter?

Think of perimeter as the fence around a garden. You need to add up all the sides to know how much fencing to buy: length + width + length + width.

Can I use P = 2l + 2w instead of P = 2(l + w)?

Yes, both formulas work perfectly! P = 2l + 2w = 2(15) + 2(7) = 30 + 14 = 44. Use whichever formula feels easier for you.

What if the rectangle had different dimensions?

The process stays the same! Just substitute the new values into the formula. For example, if length = 12 and width = 8, then P = 2(12 + 8) = $2 \times 20 = 40$ .

How can I check if my perimeter answer makes sense?

Your perimeter should always be larger than any single side. Since our longest side is 15, and our perimeter is 44, this makes sense because 44 > 15.

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