Diagonals: Calculation of the diagonal using properties

Question 1

Look at the following rectangle:

AB = 12

AC = 13

Calculate the area of the triangle BCD.

Question 2

Look at the following rectangle:

BD = 17

Calculate the length of the diagonal AC.

Question 3

Given the following rectangle:

O is the intersection point of the diagonals.

Given: BO=5

Calculate the length of the diagonal BD.

Question 4

Look at the following rectangle:

O is the intersection point of the diagonals.

BO = 5

Calculate the length of the diagonal AC.

Question 5

Look at the following rectangle:

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

AO = O

D = 6.5

Calculate the length of the diagonal AC.

Examples with solutions for Diagonals: Calculation of the diagonal using properties

Exercise #1

Look at the following rectangle:

AB = 12

AC = 13

Calculate the area of the triangle BCD.

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Use the Pythagorean Theorem to calculate the length of $AD$ .
Step 2: Calculate the area of triangle $\triangle BCD$ .

Step 1: Given $AB = 12$ and $AC = 13$ , we use the Pythagorean Theorem to find $AD$ .

AC^2 = AB^2 + AD^2 \implies 13^2 = 12^2 + AD^2

169 = 144 + AD^2 \implies AD^2 = 25 \implies AD = 5

Step 2: Knowing the sides $AD = 5$ (height of the rectangle) and $AB = 12$ (base of the rectangle), triangle $\triangle BCD$ will have the base $BC = 12$ and the height $BD = 5$ .

The area of triangle $\triangle BCD$ is:

\text{Area}_{\triangle BCD} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times 5 = 30

Therefore, the area of triangle $\triangle BCD$ is 30.

Answer

Exercise #2

Look at the following rectangle:

BD = 17

Calculate the length of the diagonal AC.

Video Solution

Answer

Exercise #3

Given the following rectangle:

O is the intersection point of the diagonals.

Given: BO=5

Calculate the length of the diagonal BD.

Video Solution

Answer

Exercise #4

Look at the following rectangle:

O is the intersection point of the diagonals.

BO = 5

Calculate the length of the diagonal AC.

Video Solution

Answer

Exercise #5

Look at the following rectangle:

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

AO = O

D = 6.5

Calculate the length of the diagonal AC.

Video Solution

Answer

Question 1

Look at the following rectangle:

AD = 3

AB = 4

Calculate the length of the diagonal AC.

Exercise #6

Look at the following rectangle:

AD = 3

AB = 4

Calculate the length of the diagonal AC.