Given I = 30 in., w = 20 in., h = 18 in., and x = 36.1 in., find the length of d. Round
the answer to the nearest tenth.
Incorrect
To find the length of d, we can use the given information and the concept of similar triangles. Let's set up a proportion using the corresponding sides of the two similar triangles.
In the first triangle, we have:
I (the length of the hypotenuse) = 30 inches (given)
w (the length of the base) = 20 inches (given)
h (the height) = 18 inches (given)
In the second triangle, we have:
I' (the length of the hypotenuse) = x (given)
w' (the length of the base) = d (the length we're trying to find)
h' (the height) = unknown
Using the concept of similar triangles, we can set up the following proportion:
I/I' = w/w' = h/h'
Plugging in the known values, we have:
30/x = 20/d = 18/h'
Now we can solve for d by cross-multiplying and isolating d:
30 * d = 20 * x
30d = 20x
d = (20x) / 30
d = 2x/3
Now, we can substitute the given value of x (36.1 inches) into the equation to find the length of d:
d = 2 * 36.1 / 3
d ≈ 72.2 / 3
d ≈ 24.07
Therefore, the length of d, rounded to the nearest tenth, is approximately 24.1 inches.
To find the length of d, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with sides of length w, h, and d.
Using the Pythagorean theorem, we can write the equation:
w^2 + h^2 = d^2
Substituting the given values:
(20 in.)^2 + (18 in.)^2 = d^2
400 in.^2 + 324 in.^2 = d^2
724 in.^2 = d^2
Taking the square root of both sides:
sqrt(724 in.^2) = sqrt(d^2)
26.909525466974098 in. = d
Rounding to the nearest tenth:
d ≈ 26.9 in.
Apologies for the incorrect answer. Let's try solving it correctly.
To find the length of d, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with sides of length w, h, and d.
Using the Pythagorean theorem, we can write the equation:
w^2 + h^2 = d^2
Substituting the given values:
(20 in.)^2 + (18 in.)^2 = d^2
400 in.^2 + 324 in.^2 = d^2
724 in.^2 = d^2
Taking the square root of both sides:
d = sqrt(724 in.^2)
d ≈ 26.93 in. (rounded to two decimal places)
Therefore, the length of d is approximately 26.93 inches.