## Description

Directions: Solve each of the following problems.

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## Explanation & Answer

The solutions are ready. Please note that the questions 3 has only 1 right triangle of two, while the question 7 has no right triangles. I had to find their areas using Heron's formula.

24

1. The largest side of the first triangle is 6, thus the second triangle is

6

= 4 times greater.

This way the perimeter of the second triangle is (2 + 4 + 6) ∙ 4 = 𝟒𝟖.

[note that 2, 4, 6 is not a so good triangle]

2. The ratio of areas is the ratio of sides squared.

Thus, the ratio of sides is √64: √81 = 𝟖: 𝟗.

3. The area of the first triangle is

1

2

∙ 8 ∙ 6 = 24.

5 2

𝟐𝟎𝟎

If a triangle has a ratio 3: 5 to the given, its area is 24 ∙ ( ) =

3

𝟑

.

The second triangle is not right because 102 + 82 ≠ 122 .

1

Use Heron’s formula: 𝑠 = 2 (8 + 10 + 12) = 15, the area is √15 ∙ 7 ∙ 5 ∙ 3 = 15√7.

5 2

𝟏𝟐𝟓√𝟕

If a triangle has a ...