Problem Analysis:
The image contains three geometry problems. Let's solve each one step by step.
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####
Problem 1:
Question: The edge of a right triangle is 8 cm long and its hypotenuse is 6 cm. What is the area of the triangle?
Solution:
1.
Identify the given information:
- One leg of the right triangle is 8 cm.
- The hypotenuse is 6 cm.
2.
Analyze the situation:
- In a right triangle, the hypotenuse is always the longest side. However, here the hypotenuse (6 cm) is shorter than one of the legs (8 cm). This is impossible because the hypotenuse must be longer than either leg in a right triangle.
- Therefore, the problem as stated is
not possible under the rules of geometry.
3.
Conclusion:
- The problem is invalid because it violates the properties of a right triangle.
---
####
Problem 2:
Question: A square has a total of 10 feet of fencing around it. If the sum of its angles is 720 degrees, how many more sides does a polygon have if the sum of its angles is 900 degrees?
Solution:
1.
Identify the given information:
- The square has a perimeter of 10 feet.
- The sum of the interior angles of the square is 720 degrees.
- We need to find how many more sides a polygon has if the sum of its angles is 900 degrees.
2.
Sum of Interior Angles Formula:
- The sum of the interior angles of a polygon with \( n \) sides is given by:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
3.
Calculate the number of sides for the polygon with a sum of 720 degrees:
\[
720 = (n - 2) \times 180
\]
\[
n - 2 = \frac{720}{180} = 4
\]
\[
n = 4 + 2 = 6
\]
- So, the polygon with a sum of 720 degrees has 6 sides.
4.
Calculate the number of sides for the polygon with a sum of 900 degrees:
\[
900 = (n - 2) \times 180
\]
\[
n - 2 = \frac{900}{180} = 5
\]
\[
n = 5 + 2 = 7
\]
- So, the polygon with a sum of 900 degrees has 7 sides.
5.
Determine how many more sides the second polygon has:
\[
7 - 6 = 1
\]
6.
Conclusion:
- The polygon with a sum of 900 degrees has
1 more side than the polygon with a sum of 720 degrees.
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####
Problem 3:
Question: If a rectangle’s area is 3,000 square feet and its length is 60 feet, what is its perimeter?
Solution:
1.
Identify the given information:
- Area of the rectangle = 3,000 square feet.
- Length of the rectangle = 60 feet.
2.
Formula for the area of a rectangle:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
\[
3,000 = 60 \times \text{Width}
\]
3.
Solve for the width:
\[
\text{Width} = \frac{3,000}{60} = 50 \text{ feet}
\]
4.
Formula for the perimeter of a rectangle:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
\]
\[
\text{Perimeter} = 2 \times (60 + 50) = 2 \times 110 = 220 \text{ feet}
\]
5.
Conclusion:
- The perimeter of the rectangle is
220 feet.
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Final Answers:
1.
Not possible (invalid problem).
2.
1 more side.
3.
220 feet.
\[
\boxed{1, 1, 220}
\]
Parent Tip: Review the logic above to help your child master the concept of test of genius worksheet.
