Calculate Rectangle Diagonal: Finding AC Length in 3×4 Rectangle

Look at the rectangle ABC is below.

AB = 4

AD = 3

Determine the length of the diagonal AC?

444333AAABBBCCCDDDMMM

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate AC
00:03 Opposite sides are equal in a rectangle
00:07 Side values according to the given data
00:11 Opposite sides are equal in a rectangle
00:15 Side values according to the given data
00:21 We'll use the Pythagorean theorem in triangle ABC
00:32 We'll substitute appropriate values and solve for AC
00:41 And this is the solution to the problem

Step-by-step written solution

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1

Understand the problem

Look at the rectangle ABC is below.

AB = 4

AD = 3

Determine the length of the diagonal AC?

444333AAABBBCCCDDDMMM

2

Step-by-step solution

In a rectangle, each pair of opposite sides are equal to each other, therefore:

AB=DC=4 AB=DC=4

We will use the Pythagorean theorem to find AC:

AC2=BC2+DC2 AC^2=BC^2+DC^2

Let's substitute the known data:

AC2=32+42 AC^2=3^2+4^2

AC2=9+16 AC^2=9+16

AC2=25 AC^2=25

Let's take the square root:

AC=25=5 AC=\sqrt{25}=5

3

Final Answer

5 5

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

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