The perimeter of a triangle is 110 inches. The ratio of the side measures are 6:7:9. Find the measure of each side.
1 answer:
The ratio of the side measures are 6:7:9.
Let's assume length of three sides of the triangle is 6x, 7x and 9x.
Given,perimeter of a triangle is 110 inches.. Perimeter is the sum of all three sides of the triangle. So, we can set up an equation as follows:
6x+7x+9x= 110
22x =110
Dividing each sides by 22.
x=5.
Now we can plug in x=5 in all the expressions of sides.
So, 6x=6(5)=30,
7x=7(5)=35
9x=9(5)=45.
So, the sides of the triangle are 30 inches, 35 inches and 45 inches.
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To solve this problem, you must find the altitude, represented by a dashed line in this picture.
To do this, use the Pythagorean theorem: a^2 + b^2 = c^2
The hypotenuse (longest side in a triangle) is always the c value. So plug that into your equation for c.
This leaves you with:
a^2 + b^2 = 10^2
Next, plug in your one side length of the triangle that you have besides the hypotenuse, which is a 5. This will be your b value.
This leaves you with:
a^2 + 5^2 = 10^2
After that, square your number values to simplify the equation. To square a number, you multiply it by itself. In this case, 5 x 5 = 25 and 10 x 10 = 100.
So when you rewrite your equation you have:
a^2 + 25 = 100
To start to isolate your variable, subtract 25 on both sides of the equation to keep it balanced.
This results in:
a^2 = 75
To isolate your variable, square root the a variable and square root the other side to keep it balanced. A square root cancels out a square, so that’s how you know you can do this.
Since 75 isn’t a perfect square, find the highest perfect square that’s able to be multiplied to get 75. This is 25. 25 x 3 = 75 so put that under a radical sign.
After that, simplify the radical by taking the perfect square out of the “jail” (square root sign) this causes the perfect square to be square-rooted as it moves across to the other side of the sign. So, your final answer has a five on the outside of the radical sign with a 3 left inside.
So your final answer is:
5 radical sign 3.
(I apology for e lack of math symbols, I am on the road on vacation so I am on mobile.
I hope this still helps! :)
To do this, use the Pythagorean theorem: a^2 + b^2 = c^2
The hypotenuse (longest side in a triangle) is always the c value. So plug that into your equation for c.
This leaves you with:
a^2 + b^2 = 10^2
Next, plug in your one side length of the triangle that you have besides the hypotenuse, which is a 5. This will be your b value.
This leaves you with:
a^2 + 5^2 = 10^2
After that, square your number values to simplify the equation. To square a number, you multiply it by itself. In this case, 5 x 5 = 25 and 10 x 10 = 100.
So when you rewrite your equation you have:
a^2 + 25 = 100
To start to isolate your variable, subtract 25 on both sides of the equation to keep it balanced.
This results in:
a^2 = 75
To isolate your variable, square root the a variable and square root the other side to keep it balanced. A square root cancels out a square, so that’s how you know you can do this.
Since 75 isn’t a perfect square, find the highest perfect square that’s able to be multiplied to get 75. This is 25. 25 x 3 = 75 so put that under a radical sign.
After that, simplify the radical by taking the perfect square out of the “jail” (square root sign) this causes the perfect square to be square-rooted as it moves across to the other side of the sign. So, your final answer has a five on the outside of the radical sign with a 3 left inside.
So your final answer is:
5 radical sign 3.
(I apology for e lack of math symbols, I am on the road on vacation so I am on mobile.
I hope this still helps! :)
First we have to assume that each quarter touched each other. Hence the area of the table not covered by the coins (A) is equal to the total area of the table (At) minus the total area of the coins (Ac). Coins are circle, so 
and r =24.26mm. The area of one coin is then 1848.98mm^2. Hence the equation is A = At - xAc where x is the number of coins.
Step-by-step explanation:
let the speed of diesel train = x
the equation would be:
(2+6)x = 6(x+15)
8x = 6x+90
8x-6x = 90
2x = 90
x = 90/2
x = 45
Therefore, the speed of diesel train =
45 mph
