A kite has two perpendicular interior

diagonals. One diagonal has a

measurement of 17 cm and the area of the

kite is 51 cm2. Find the sum of the two

perpendicular interior diagonals.

To find the sum of the two perpendicular interior diagonals of the kite, we need to determine the length of the unknown diagonal.

Given:
1. One diagonal (\(d_1\)) is 17 cm.
2. The area of the kite (\(A\)) is 51 cm\(^2\).

The formula for the area of a kite with perpendicular diagonals is:
\[
A = \frac{1}{2} \times d_1 \times d_2
\]

We can rearrange this formula to solve for the unknown diagonal (\(d_2\)):
\[
51 = \frac{1}{2} \times 17 \times d_2
\]

To isolate \(d_2\), multiply both sides by 2:
\[
102 = 17 \times d_2
\]

Now, divide both sides by 17:
\[
d_2 = \frac{102}{17} = 6
\]

Now that we have the lengths of both diagonals (\(d_1 = 17\) cm and \(d_2 = 6\) cm), we can find the sum of the two diagonals:
\[
d_1 + d_2 = 17 + 6 = 23
\]

Thus, the sum of the two perpendicular interior diagonals is \(23\) cm.

Would you like further details or have any questions?

Here are 8 related questions that expand on the previous information:
1. How do you derive the formula for the area of a kite using its diagonals?
2. What are the properties of the diagonals in a kite?
3. How can you verify the area calculation of a kite?
4. If the area of a kite is known, how can you find the lengths of the diagonals?
5. What are the implications of changing one diagonal's length on the kite's area?
6. How would you find the length of the other diagonal if only one diagonal and the area are known?
7. What happens to the area of a kite if both diagonals are increased by a factor of 2?
8. How do perpendicular diagonals affect the symmetry of a kite?

**Tip:** Always check your calculations and consider alternative methods to verify your results for accuracy.

Learn how to find the sum of two perpendicular interior diagonals of a kite with one diagonal measuring 17 cm and an area of 51 cm². This problem involves geometry, including the area calculation of a kite and properties of perpendicular diagonals. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation