Based on the given segment lengths, determine whether the segments can form a triangle.

Mathematics

1 answer:

murzikaleks [220]3 years ago

4 0

For 3 sides to form a triangle two sides added together need to be greater then the 3rd side. You need to check all 3 combinations:

1. 11.5 + 10.5 = 22, 22> 6.1

11.5 + 6.1 = 17.6 17.6 > 10.5

10.5 + 6.1 = 16.6, 16.6 > 11.5

This one can make a triangle.

2. 9.5 + 3.5 > 4.5

9.5 + 4.5 > 3.5

4.5 + 3.5 < 9.5

Cannot make a triangle.

3. 8 + 6.7 > 1

6.7 + 1 < 8

Cannot make a triangle.

4. Can make a triangle

5. Can

6. Can

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Help please, tank u :)

elena-s [515]

Answer:

16 ft

Step-by-step explanation:

Let the width of the rectangle be x ft

Therefore, length = (x + 2) ft

Area of the rectangle = 15 square ft

$x(x + 2) = 15 \\ \\ {x}^{2} + 2x = 15 \\ \\ {x}^{2} + 2x - 15 = 0 \\ \\ {x}^{2} + 5x - 3x - 15 = 0 \\ \\ x(x + 5) - 3(x + 5) = 0 \\ \\ (x + 5)(x - 3) = 0 \\ \\ x + 5 = 0 \: or \: \: x - 3 = 0 \\ \\ x = - 5 \: \: or \: \: x = 3 \\ \\ \because \: x \: can \: not \: be \: - ve \\ \\ \therefore \: x = 3 \\ \\ \implies \: x + 2 = 3 + 2 = 5 \\ \\ perimeter \: of \: rectngle \\ = 2(5 + 3) \\ = 2 \times 5 \\ = 16 \: ft$