Calculate the Perimeter of Rectangle ABCD with Sides 24 and 25 Units

Rectangle Perimeter with Pythagorean Theorem

AAABBBCCCDDD2524Calculate the perimeter of the rectangle ABCD.

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1

Understand the problem

AAABBBCCCDDD2524Calculate the perimeter of the rectangle ABCD.

2

Step-by-step solution

Let's focus on triangle BCD in order to find side BC.

We'll use the Pythagorean theorem using our values:

BC2+DC2=BD2 BC^2+DC^2=BD^2

BC2+242=252 BC^2+24^2=25^2

BC2=625576=49 BC^2=625-576=49

Let's now remove the square root:

BC=7 BC=7

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

DC=AB=24 DC=AB=24

BC=AD=7 BC=AD=7

Now we can calculate the perimeter of the rectangle by adding all sides together:

24+7+24+7=14+48=62 24+7+24+7=14+48=62

3

Final Answer

62

Key Points to Remember

Essential concepts to master this topic
  • Pythagorean Theorem: In right triangles, a2+b2=c2 a^2 + b^2 = c^2 where c is hypotenuse
  • Rectangle Properties: Opposite sides are equal: AB = DC = 24, BC = AD = 7
  • Verification: Check diagonal: 72+242=49+576=625=252 7^2 + 24^2 = 49 + 576 = 625 = 25^2

Common Mistakes

Avoid these frequent errors
  • Using diagonal as a side in perimeter calculation
    Don't add the diagonal 25 to calculate perimeter = 24 + 7 + 24 + 25 = 80! The diagonal is inside the rectangle, not part of the boundary. Always use only the four outer sides for perimeter: 24 + 7 + 24 + 7 = 62.

Practice Quiz

Test your knowledge with interactive questions

The points A and O are shown in the figure below.

Is it possible to draw a rectangle so that the side AO is its diagonal?

AAAOOO

FAQ

Everything you need to know about this question

Why can't I just add 24 + 25 + 24 + 25 for the perimeter?

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Because 25 is the diagonal, not a side! The diagonal cuts through the inside of the rectangle. For perimeter, you only count the boundary - the four outer edges that form the rectangle's outline.

How do I know which sides are equal in a rectangle?

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In rectangles, opposite sides are always equal. So if you know AB = 24, then the opposite side DC also equals 24. Same for the other pair: BC = AD.

Why do we use the Pythagorean theorem here?

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The diagonal creates a right triangle inside the rectangle. We know the diagonal (25) and one side (24), so we can find the unknown side using a2+b2=c2 a^2 + b^2 = c^2 .

What if I get a negative number under the square root?

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That means you made an error! In this problem: BC2=252242=625576=49 BC^2 = 25^2 - 24^2 = 625 - 576 = 49 . Always subtract the smaller square from the larger square.

Can I solve this without the Pythagorean theorem?

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No, because you need to find the unknown side first. The diagram only shows one side length (24) and the diagonal (25). The Pythagorean theorem is the key to finding the missing side.

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