## Homework 3 Isosceles & Equilateral Triangles Answer Key Introduction:

Geometry can be a challenging subject, but don’t worry, we have your back! This blog post provides the answer key to Homework 3 on Isosceles and Equilateral Triangles. By the end of this post, you’ll have a better understanding of the concepts and will be ready to tackle any geometry problem that comes your way.

### Blog Body:

Question 1: An isosceles triangle has a base of 12 cm and legs of 8 cm. Find the height of the triangle.

Solution: There are different formulas for finding the height of an isosceles triangle, but we can use the Pythagorean Theorem.

Using the theorem a² + b² = c², where a and b are the legs, and c is the hypotenuse (the base in this case), we get:

8² + h² = 12²

64 + h² = 144

h² = 144 – 64

h = √80 = 8√5 cm

Answer: The height of the triangle is 8√5 cm.

Question 2: A right equilateral triangle has a hypotenuse of 10 cm. Find the length of a leg.

Solution: Since it is an equilateral triangle, all the sides have the same length, so let’s call the length x. Using the Pythagorean Theorem, we can find x.

a² + b² = c²

x² + x² = 10²

2x² = 100

x² = 50

x = √50 = 5√2 cm

Answer: The length of a leg is 5√2 cm.

Question 3: An equilateral triangle has a perimeter of 72 cm. Find the length of one side of the triangle.

Solution: Since it is an equilateral triangle, all the sides have the same length, so let’s call the length x. The perimeter of the triangle is the sum of the three sides, so:

3x = 72

x = 24

Answer: The length of one side of the triangle is 24 cm.

Question 4: An isosceles triangle has a base of 6 cm and a height of 8 cm. Find the length of the legs.

Solution: We can use the Pythagorean Theorem to find the length of the legs.

Using the theorem a² + b² = c², where a and b are the legs, and c is the hypotenuse (in this case, it’s the line that connects the midpoint of the base to the top of the triangle, which is also the height), we get:

a² + (8)² = b²

a² + 64 = b²

Since it’s an isosceles triangle, the legs have the same length, so we can set a = b and solve the equation.

a² + 64 = a²

64 = 0 (not possible)

This means that there is no possible isosceles triangle with a base of 6 cm and a height of 8 cm. Therefore, the answer is “no triangle.”

Answer: No triangle exists with these measurements.

Question 5: An equilateral triangle has a perimeter of 30 cm. Find the area of the triangle.

Solution: We can use the formula for the area of an equilateral triangle, which is A = √3/4 x a², where a is the length of the sides.

Since the perimeter of the triangle is 30 cm, we know that the length of each side is 10 cm (since there are three sides). Substituting this into the formula, we get:

A = √3/4 x (10²)

A = √3/4 x 100

A = 25√3

Answer: The area of the triangle is 25√3 cm².

### Conclusion:

Geometry is a fascinating subject, and with the right resources, it can be enjoyable too! We hope that this answer key to Homework 3 on Isosceles and Equilateral Triangles has helped you understand the concepts and that you are on your way to acing your geometry homework. Don’t forget to practice regularly and reach out to your teacher for help if you need it. Happy problem-solving!