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Stella [2.4K]
3 years ago
9

Determine whether the given measures can be the lengths of the sides of a triangle. write yes or no. explain. 9.2, 14.5, 17.1

Mathematics
2 answers:
viktelen [127]3 years ago
8 0

Answer with explanation:

If the length of three segments are, 9.2, 14.5 and 17.1 ,it can be sides of triangle if , Sum of two segments is greater than the third segment.

1.→ 9.2 +14.5=23.7 >17.1

2.→ 14.5 +17.1=41.6 > 9.2

3.→17.1 +9.2=26.3 >14.5

As, sum of any two segment is greater than third segment, so the following measurements can be the the lengths of the sides of a triangle.  

Sergio039 [100]3 years ago
3 0
If the triangle has a angle of 90°, you can solved this exercise by applying the Pythagorean Theorem, which is:

 h²=a²+b²
 h=√(a²+b²)

 h: It is the hypotenuse (The opposite side of the right angle and the longest side of the triangle).

 a and b: They are the legs (The sides that form the right angle).

 The result of h=√(a²+b²), should be 17.1 (The longest side given in the problem). So, let's substitute the values of the legs into the Pythagorean equation:

 h=√(a²+b²)
 h=√((9.2)²+(14.5)²)
 h=17.1

 Therefore, the answer is:

 Yes, the given measures can be the lengths of the sides of a triangle.
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<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : l*w, where b = length and w =width. The question gives that the area is 18 in².

For this question, the length exceeds its width by 17 inches - l=w+17. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=l*w

18=(w+17)*w

18=w²+17w

w²+17w-18=0

Next step will be solve the previous equation ( W²+17W-18=0)

w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}

Therefore,

w_1=\frac{-17+19}{2\cdot \:1}=1\\ \\ \\ w_2=\frac{-17-19}{2\cdot \:1}=-18

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², you have.

18=l*w

18=l*1

l=18 in

Read more about the area of rectangle here:

brainly.com/question/25292087

#SPJ1

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