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3 years ago

Apply the Pythagorean Theorem to find the distance between points B and C.

Mathematics

2 answers:

lys-0071 [83]3 years ago

6 0

The option B $\boxed{{\mathbf{10 units}}}$ is correct.

Further explanation:

The PythagoreanTheorem is used in the right angle triangle and it states that the square of the hypotenuse is equal to the sum of the squares of the perpendicular and base.

It can be mathematically expressed as,

${h^2} = {p^2} + {b^2}$

Here, $h$ is the hypotenuse, $p$ is the perpendicular and $b$ is the base.

Step by step explanation:

Step 1:

It is observed from given figure that after joining the points $A,B{\text{ and C}}$ it is established as right angle triangle.

First determine the perpendicular and the base of the triangle.

It can be seen that there are 8 boxes between the point $A{\text{ and }}C$ and 6 boxes between the point $A{\text{ and B}}$ .

Therefore, the base of the triangle $AC$ is ${\text{8 units}}$ and the perpendicular of the triangle $AB$ is ${\text{8 units}}$ .

Step 2:

Now use the Pythagoras theorem to find the distance between $B{\text{ and }}C$ .

The distance between $B{\text{ and }}C$ is the length of the hypotenuse of the triangle $ABC$ .

The length of the hypotenuse $BC$ can be calculated as,

$\begin{aligned}{h^2}&= {p^2} + {b^2}\\{h^2}&= {6^2} + {8^2}\\{h^2} &= 100\\h&= 10\\\end{aligned}$

Therefore, the distance between $B{\text{ and }}C$ is 10 units.

Thus, option B 10 units is correct.

Learn more:

Learn more about the function is graphed below brainly.com/question/9590016
Learn more about the symmetry for a function brainly.com/question/1286775
Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Pythagoras theorem.

Keywords: Distance, Pythagoras theorem, points, base, perpendicular, hypotenuse, right angle triangle, boxes, units, squares, sum,

Lyrx [107]3 years ago

3 0

10 units

6^+8^=X^

36+64=x^

100=x^

10=x

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Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.

<h3>What is the Pythagorean Theorem?</h3>

The Pythagorean Theorem relates the length of the legs $l_1$ and $l_2$ of a right triangle with the length of the hypotenuse h, according to the following equation:

$h^2 = l_1^2 + l_2^2$

Researching this problem on the internet, we have that:

The unknown side length is of a leg of x.

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The hypotenuse is of 12 cm.

Hence:

x² + 9² = 12²

x = sqrt(12² - 9²)

x = 7.9 cm.

The unknown side length of the triangle is of 7.9 cm.

More can be learned about the Pythagorean Theorem at brainly.com/question/654982

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2 years ago

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3 years ago

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Answer:

See answers below for explanations (answers are in bold)

Step-by-step explanation:

Problem 1 (Top left):

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We can make this irregular shape into a half-ellipse and a rectangle. We would find their separate areas and add them up. The area of the half-ellipse would be A=1/2πab. The value of "a" would be 13.8/2=6.9 since that's the length of the rectangle. The value of "b" would be 3.5, so that means the area of the half-ellipse would be A = 1/2(π)(6.9)(3.5) = 12.075π = 37.935 units^2. The width and length of the rectangle are 5.4 and 13.8 respectively, so this means the area of the rectangle is 5.4*13.8 = 74.52 units^2. Combining both areas, we get 37.935+74.52 = 112.455 units^2 as our final answer

Problem 4 (Bottom right):

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Answer:

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Step-by-step explanation:

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