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juin [17]
2 years ago
13

The sides of a triangle are in the ratio 3, 4, 5. State whether the triangle is right angled or not.

Mathematics
2 answers:
kvv77 [185]2 years ago
5 0

Answer:

If the sides of a triangle are in the ratio 3:4:5, prove that it is a right-angled triangle.

Step-by-step explanation:

In order to prove that the triangle is a right-angled triangle or not, take the ratio as the length of the sides then consider the triangle to be a right-angled triangle, then prove the Pythagoras theorem. If the sides satisfy the Pythagoras theorem, then it’s a right-angled triangle otherwise, it’s not a right-angled triangle.

We are given the sides of a triangle whose ratio is 3:4:5.

Considering the sides to be 3x,4x,5x.

Since, we know that the length of hypotenuse is always greater than the other two sides, so we are taking the hypotenuse to be 5x and other remaining sides to be 3x and 4x.

We are only considering that the given triangle is a right-angled triangle. For that we need to prove that the sides follow Pythagoras theorem.

So, for Pythagora's theorem, we know that the sum of the square of the base side and square of the height side is equal to the square of the hypotenuse.

Squaring the base side 4x, we get:

(4x)2=16x2 …….(1)

Similarly, squaring the height side 3x, we get:

(3x)2=9x2 …….(2)

Squaring the hypotenuse side 5x, and we get:

(5x)2=25x2 …….(3)

Taking the sum of (1) and (2):

16x2+9x2=25x2, which is equal to the equation (3).

That means the sum of the square of base and the square of height is equal to the square of hypotenuse, that satisfies the Pythagoras theorem, that implies the triangle ABC is actually a right-angled triangle, which is right-angled at B. And this proves our consideration to be true.

kramer2 years ago
3 0

Answer:

it is a right triangle

Step-by-step explanation:

If the triangle is a right triangle, it will meet the Pythagorean theorem

a^2 + b^2 = c^2

3^2+4^2 = 5^2

9+16=25

25=25

This is true so it is a right triangle

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H
tigry1 [53]

Answer:

4448 feet²

Step-by-step explanation:

Using the formula A = 2((l)x(w) + (l)x(h) + (w)x(h)) we can take the length, width and height and plug them in. A = 2(44x21 + 44x20 + 21x20), solving this equation we get 4448 feet^{2}.

8 0
2 years ago
Round to 2 decimal places *
EleoNora [17]

Answer: The circumference of the dome is therefore 149.15 feet or 47.5π feet

Step-by-step explanation:

A scale is basically referred to as the ratio of the dimensions of an object as represented in a draft to the real or true dimensions of the object being drafted.

The figure(s) on the left of the ratio sign represents the size and dimensions of the model with respect to the actual size or dimensions of the object. On the other hand, the figure on the right hand size represents the actual dimensions and size of the real object.

So, if an object is being drawn with the ratio, 1cm : 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always be represented by 1cm in the drawing. If the object is being drawn with a scale of 5cm : 1cm then the actual size of the object will be increased in the drawing. That is, for every 1cm in the actual dimensions of the object, there will be a 5cm representation in the drawing.

Now, the architect draws with a scale of 0.25 inches : 1 foot. If the diameter of the hemispherical dome is 23.75 inches in the scale model, then the actual diameter of the dome is:

0.25 inches ------- 1 foot

23.75 inches ------- ? feet

= 23.75/0.25 × 1

= 95 feet

Therefore, the actual diameter of the dome is 95 feet. We are now required to find the circumference of this dome.

The dome is a hemisphere which literally means half of a sphere. So, if the formula for finding the circumference of a sphere is πd, that of a hemisphere will then be πd/2. Since the diameter is already known to be 95 feet, the circumference of the hemisphere =

(π × 95)/2

=47.5π feet

Or

If π = 3.14, then the circumference = (3.14 × 95)/2 = 149.15 feet

The circumference of the dome is 149.15 feet or 47.5π feet

5 0
3 years ago
Sam is renting one of two cars to go on a 300-mile trip. The first car can travel 75 miles on 5 gallons of gas. The second car c
djverab [1.8K]
First let’s establish a few things, The first car can travel 300 miles with 20 gallons of gas, if 14 gallons of gas costs 49.49 then for ever gallon of gas Sam is paying 3 dollars and 53.5 cents. That means for 20 gallons, Sam will need around 71$ for the entire trip if he uses the first car.
8 0
2 years ago
Given x∥y and m∠2=23° .<br><br> What is m∠7?<br><br> Enter your answer in the box.
malfutka [58]

Answer:

angle2=23°

angle7=angle5

angle2=angle6

so,angle8=23°

total angle = 180°

angle7=180°-46°=134°÷2=67°

3 0
3 years ago
Newborn babies: A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights
Fed [463]

Answer:

a) 615

b) 715

c) 344

Step-by-step explanation:

According to the Question,

  • Given that,  A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 732 babies born in New York. The mean weight was 3311 grams with a standard deviation of 860 grams

  • Since the distribution is approximately bell-shaped, we can use the normal distribution and calculate the Z scores for each scenario.

Z = (x - mean)/standard deviation

Now,

For x = 4171,  Z = (4171 - 3311)/860 = 1  

  • P(Z < 1) using Z table for areas for the standard normal distribution, you will get 0.8413.

Next, multiply that by the sample size of 732.

  • Therefore 732(0.8413) = 615.8316, so approximately 615 will weigh less than 4171  

 

  • For part b, use the same method except x is now 1591.    

Z = (1581 - 3311)/860 = -2    

  • P(Z > -2) , using the Z table is 1 - 0.0228 = 0.9772 . Now 732(0.9772) = 715.3104, so approximately 715 will weigh more than 1591.

 

  • For part c, we now need to get two Z scores, one for 3311 and another for 5031.

Z1 = (3311 - 3311)/860 = 0

Z2 = (5031 - 3311)/860= 2  

P(0 ≤ Z ≤ 2) = 0.9772 - 0.5000 = 0.4772

  approximately 47% fall between 0 and 1 standard deviation, so take 0.47 times 732 ⇒ 732×0.47 = 344.

5 0
2 years ago
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