Find the value of x. Give your answer in simplest radical form.
1 answer:
Answer: x = 5*sqrt(10)
"sqrt" stands for "square root"
-------------------------------------------------------
Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively)
The length y is the bottom horizontal leg for the triangle on the right.
The length z is the bottom horizontal leg for the triangle on the left.
To find x, we need to find y first, which will help us find z, and then we can finally get to x.
Let's find y first
To do this, we use the pythagorean theorem
a^2 + b^2 = c^2
y^2 + 9^2 = 15^2
y^2 + 81 = 225
y^2 + 81-81 = 225-81
y^2 = 144
sqrt(y^2) = sqrt(144)
y = 12 ... keep in mind that y is a length, so it needs to be positive
Notice how the y and z lengths combine to form a total length of 25 units
Therefore,
y+z = 25
12+z = 25
12+z-12 = 25-12
z = 13
Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time
a^2 + b^2 = c^2
z^2 + 9^2 = x^2
13^2 + 9^2 = x^2
169 + 81 = x^2
250 = x^2
x^2 = 250
sqrt(x^2) = sqrt(250)
x = sqrt(250)
x = sqrt(25*10)
x = sqrt(25)*sqrt(10)
x = 5*sqrt(10)
This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x
Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately
"sqrt" stands for "square root"
-------------------------------------------------------
Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively)
The length y is the bottom horizontal leg for the triangle on the right.
The length z is the bottom horizontal leg for the triangle on the left.
To find x, we need to find y first, which will help us find z, and then we can finally get to x.
Let's find y first
To do this, we use the pythagorean theorem
a^2 + b^2 = c^2
y^2 + 9^2 = 15^2
y^2 + 81 = 225
y^2 + 81-81 = 225-81
y^2 = 144
sqrt(y^2) = sqrt(144)
y = 12 ... keep in mind that y is a length, so it needs to be positive
Notice how the y and z lengths combine to form a total length of 25 units
Therefore,
y+z = 25
12+z = 25
12+z-12 = 25-12
z = 13
Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time
a^2 + b^2 = c^2
z^2 + 9^2 = x^2
13^2 + 9^2 = x^2
169 + 81 = x^2
250 = x^2
x^2 = 250
sqrt(x^2) = sqrt(250)
x = sqrt(250)
x = sqrt(25*10)
x = sqrt(25)*sqrt(10)
x = 5*sqrt(10)
This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x
Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately
You might be interested in
Answer = 55,25 inches
Solution -
let's take x as length and y as width of the metal piece. As per the question x is 30 more than y,
⇒ x = y + 30
Then four square pieces of side 6 are cut from each corner,
so the new length and width are
x-12 , y-12
Then the volume of the new box created will be
(x-12)(y-12)6
in the question the volume of the given figure is given to be 3354
so (x-12)(y-12)6 = 3354
putting the value of x in the the above equation
⇒ (y+30 - 12)(x-12) = 3354/6 = 559
⇒ (y+18)(y-12) = 559
⇒ y² + 6y - 775 = 0
⇒ y² + 31y - 25y -775 = 0
⇒ (y+31)(y-25) = 0
⇒ y = -31, 25
as length can not be -ve , so y = 25
then x = 25+30 = 55
Hence the dimensions of the metal piece are 55, 25 inches
