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Nezavi [6.7K]
2 years ago
8

How to use pythagorean theorem to find isosceles triangle side lengths.

Mathematics
1 answer:
Alja [10]2 years ago
7 0

Answer:

a^2 + b^2 = c^2, where c is the hypotenus and a and b are the legs

Step-by-step explanation:

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The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. What is the distance between the point of inte
malfutka [58]

1. The area of the rhombus can be found by the formula

A=\dfrac{d_1\cdot d_2}{2}, where d_1,\ d_2 are rhombus's diagonals.

Note that d_1=4.5\ dm=45\ cm, then

540=\dfrac{45\cdot d_2}{2},\\ \\540\cdot 2=45d_2,\\ \\d_2=24\ cm.

2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs

\dfrac{d_1}{2}=22.5\ cm,\ \dfrac{d_2}{2}=12\ cm.

The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem

\text{rhombus's side}^2=(22.5)^2+12^2=506.25+144=650.25,\\ \\\text{rhombus's side}=25.5\ cm.

3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.

Use twice the Pythagorean theorem to find this height:

\left\{\begin{array}{l}x^2+h^2=12^2\\(25.5-x)^2+h^2=22.5^2,\end{array}\right.

where x is projection of leg 12 cm and h is height.

Subtract the first equation from the second:

(25.5-x)^2+h^2-x^2-h^2=22.5^2-12^2,\\ \\650.25-51x=506.25-144,\\ \\51x=650.25-362.25=288,\\ \\x=\dfrac{96}{17}\ cm.

Then

h^2=144-\left(\dfrac{96}{17}\right)^2=144-\dfrac{9216}{289}=\dfrac{32400}{289},\\ \\h=\dfrac{180}{17}\ cm.

Answer: h=\dfrac{180}{17}\ cm.

7 0
3 years ago
Read 2 more answers
How do I find X for 3x-7=5x-13?
Westkost [7]
3x - 7 = 5x - 13
-3x        -3x

5x - 3x = 2x

-7 = 2x - 13
+7         +7

-13+7 = -6

2x = -6
2x/2 = -6/2
x = -3

Answer: x = -3
6 0
3 years ago
Refer the diagram at the right. identify each angle pair as adjacent, vertical, or neither 7-12
Oxana [17]
Adjacent angles are angles that are side by side (right next to each other).  They share a side.  #7 and 11 are pairs of adjacent angles.

Vertical angles are angles that are directly across from each other.  They are the same angle.  #8 and 9 are vertical angles.

#10 and 12 do not fit either of these descriptions so they are neither.
8 0
3 years ago
Can someone please how to do fractions in the lowest terms
VikaD [51]

Answer:

In order to out a fraction in lowest terms, you must divide by the Greatest Common Factor, or GCM, of the numerator and denominator in the fraction. Let's say we have the fraction 25/100. We know that the greastest common factor of 25 and 100 is 25, as 25 ÷ 25 = 1 and 100 ÷ 25 = 4 so 25/100 in lowest terms is 1/4:

25        25       1

___  ÷ ___ = ___

100      25       4

If the GCM of a fraction equals 1, the fraction is simplified. Because the only common factor of 1 and 4 is 1, we know this fraction is simplified.

1        1         1

__ ÷ ___ = ___

4        1        4

Hope this helps <3 Please contact me if your still confused

6 0
3 years ago
NEED ANSWER NOW PLEASE!
nekit [7.7K]
53,500 it that Because it’s the answer
6 0
3 years ago
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