Using the Pythagorean Theorem: Calculation using the diagonal

Look at the following rectangle:

BC = 8

BD = 17

Calculate the area of the rectangle ABCD.

We will find side DC by using the Pythagorean theorem in triangle DBC:

$BC^2+CD^2=BD^2$

Let's substitute the known data:

$8^2+CD^2=17^2$

$CD^2=289-64=225$

Let's take the square root:

$CD=15$

Now we have the length and width of rectangle ABCD and we'll calculate the area:

$15\times8=120$

120

The rectangle ABCD is shown below.

$BD=25,BC=7$

Calculate the area of the rectangle.

We will use the Pythagorean theorem in order to find the side DC:

$(BC)^2+(DC)^2=(DB)^2$

We begin by inserting the existing data into the theorem:

$7^2+(DC)^2=25^2$

$49+DC^2=625$

$DC^2=625-49=576$

Finally we extract the root:

$DC=\sqrt{576}=24$

168

ABCD is a rectangle.

AC = 13

AB = 12

Calculate the length of the side BC.

When writing the name of a polygon, the letters will always be in the order of the sides:

This is a rectangle ABCD:

This is a rectangle ABDC:

Always go in order, and always with the right corner to the one we just mentioned.

5

Below is the rectangle ABCD.

O is the intersection point of the diagonals of the rectangle.

AD = 8

BO = 8.5

Calculate the area of the triangle ABD.

According to the given information, we can claim that:

$BD=2BO=8.5\times2=17$

Now let's look at triangle ABD to calculate side AB

$AB^2+AD^2=BD^2$

Let's input the known data:

$AB^2+8^2=17^2$

$AB^2=289-64=225$

We'll take the square root

$AB=15$

Now let's calculate the area of triangle ABD:

$\frac{15\times8}{2}=\frac{120}{2}=60$

60

Calculate the perimeter of the rectangle ABCD.

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

We'll use the Pythagorean theorem and input the known data:

$BC^2+DC^2=BD^2$

$BC^2+24^2=25^2$

$BC^2=625-576=49$

Let's take the square root:

$BC=7$

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

$DC=AB=24$

$BC=AD=7$

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

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

62

Look at the following rectangle:

Calculate the perimeter of the rectangle ABCD.

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

We'll use the Pythagorean theorem and input the known data:

$BC^2+DC^2=BD^2$

$6^2+DC^2=10^2$

$DC^2=100-36=64$

Let's take the square root:

$DC=8$

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

$DC=AB=8$

$BC=AD=6$

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

$8+6+8+6=16+12=28$

28

Look at the following rectangle:

DC = 4

AC = 5

Calculate the area of the rectangle ABCD.

12

Look at the following rectangle:

Calculate the perimeter of the triangle ABD.

40

Look at the following rectangle:

Calculate the area of the triangle ABC.

30

Given the rectangle such that:

O is the intersection point of the diagonals of the rectangle.

Given: AD=6 , AB=8

Calculate the length of the section BO.

5

Below is the rectangle ABCD.

O is the intersection point of the diagonals of the rectangle.

DC = 15

OC = 8.5

Calculate the area of the rectangle ABCD.

120