The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.
<h3>What is a Triangle?</h3>
A triangle is a shape that has three sides. The sides can be measured using a ruler.
The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.
Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.
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Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Volume of a cube is length * width * height. Because it's a cube, all of these lengths are the same measurement so rather than doing V = l*w*h, we can do one of the measurements cubed, let's call it x.
So Volume = x³. So if we are given the volume, we can the length by doing the cube root.
∛125 = 5
∛216 = 6
Surface area of a cube = 6x². So now we plug both of these measurements into the formula.
For 5:
SA = 6(5)² = 6(25) = 150
For 6:
SA = 6(6)² = 6(36) = 216
The ratio of their surface areas is 150:216 or if you simplify it by dividing both by the GCF of 6, 25:36
Given :
A circle is inscribed in a square with a side length of 144.
So, radius of circle, r = 144/2 = 72 units.
To Find :
The probability that the point is inside the circle.
Solution :
Area of circle,
Area of square,
Now, probability is given by :
Therefore, the probability that the point is inside the circle is 0.785 .
