Keelie has a triangular-shaped card. The lengths of its sides are 5.1 cm, 6.8 cm, and 8.5 cm. Is the card a right triangle?

Mathematics

2 answers:

anastassius [24]2 years ago

8 0

Answer:

Yes

Step-by-step explanation:

To figure out if a triangle is a right triangle, you have to plug in the side lengths into the equation $a^{2}$ + $b^{2}$ = $c^{2}$

Your equation should look like $5.1^{2} + 6.8^{2} = 8.5^{2}$

Now you simplify. The equation should be: 26.01 + 46.24 = 72.25

Then add 26.01 and 46.24 to get 72.25 = 72.25

Since they are equal, the triangle is a right triangle.

olga nikolaevna [1]2 years ago

6 0

Answer: Yes it is a right angled triangle

Step-by-step explanation: The triangle has three sides given already which are, 8.5 cm, 6.8 cm and 5.1 cm.

In order for the triangle to qualify as a right angled triangle, the longest side must be an hypotenuse. The square of an hypotenuse must be equal to the square of the other two sides added together. This is the Pythagoras theorem, which states that

AC² = AB² + BC²

Where AC is the hypotenuse (longest side)

The longest side in this question is 8.5 cm, therefore, applying the Pythagoras theorem we now have the following expression;

8.5² = 6.8² + 5.1²

72.25 = 46.24 + 26.01

72.25 = 72.25

So, having all three sides fitted into the Pythagoras theorem, we can now conclude that the card is a right angled triangle

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Find the perimeter of a field that has length 2/x + 1 and width 5/x^2 -1.

Semmy [17]

Answer:

D)4x + 6/(x + 1)(x - 1)

Step-by-step explanation:

A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle

$p=2(l+w)$

where

$p$ is the perimeter

$l$ is the length

$w$ is the width

We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so $l=\frac{2}{x+1}$ and $w=\frac{5}{x^2-1}$ .

Replacing values:

$p=2(l+w)$

$p=2(\frac{2}{x+1} +\frac{5}{x^2-1})$

Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula $a^2-b^2=(a+b)(a-b)$ where $a$ is the first term and $b$ is the second term. We can infer that $a=x^2$ and $b=1^2$ . So, $x^2-1=(x+1)(x-1)$ . Replacing that: