peter drew a scale drawing of is room with a length of 10 inches.the actual length of his room is 13 1/9 feet.the actual length of his desk is 40 inches.approximately what is the length of the desk in the drawing
a.2/5 c.2 3/5
b.2 1/2 d. 2 7/10
We can use proportions to solve the problem.
Let x be the length of the desk in the drawing. We can set up the proportion:
10 inches (length in drawing) / x inches (length of desk in drawing) = 13 1/9 feet (actual length) / 40 inches (actual length)
Cross-multiplying, we get:
10 inches * 40 inches = x inches * 13 1/9 feet
Simplifying, we get:
x = (10 inches * 40 inches) / (13 1/9 feet)
Converting 13 1/9 feet to inches, we have:
13 1/9 feet * 12 inches/foot = 157 inches
Substituting, we get:
x = (10 inches * 40 inches) / (157 inches)
Simplifying, we get:
x ≈ 2 3/5 inches
Therefore, the approximate length of the desk in the drawing is 2 3/5 inches, which is option C.
what is the area if a circle with a diameter of 42cm
The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
To find the radius, we can divide the diameter by 2:
r = d/2 = 42 cm / 2 = 21 cm
Substituting this value into the formula, we get:
A = πr^2 = π(21 cm)^2 ≈ 1385.44 cm^2
Therefore, the area of the circle is approximately 1385.44 square centimeters.
To solve this problem, you need to set up a proportion using the given information.
Let:
Ld be the actual length of the desk
Lr be the actual length of the room
Lrd be the length of the room in the drawing
Ldd be the length of the desk in the drawing
From the problem statement, we know the following:
Lr = 13 1/9 feet = (12 * 13 + 1)/9 = 157/9 feet
Lrd = 10 inches
Ld = 40 inches
To find Ldd, the length of the desk in the drawing, we can set up the following proportion:
Ld/Lr = Ldd/Lrd
Substituting the given values, we have:
40 inches / (157/9) feet = Ldd / 10 inches
To simplify the left side of the equation, we convert 40 inches to feet:
40 inches = 40/12 feet = 10/3 feet
Now, we can substitute the converted values back into the equation:
(10/3 feet) / (157/9 feet) = Ldd / 10 inches
To divide by a fraction, we can multiply by its reciprocal:
(10/3 feet) * (9/157 feet) = Ldd / 10 inches
Simplifying the left side:
(10 * 9) / (3 * 157) feet = Ldd / 10 inches
Now, we can cross-multiply and solve for Ldd:
Ldd = (10 * 9 * 10 inches) / (3 * 157 feet)
Multiplying numerator and denominator:
Ldd = 900 inches / (471 feet)
Simplifying the fraction:
Ldd ≈ 1.912 feet
Since we want to find the length of the desk in the drawing, we need to convert 1.912 feet to inches:
1.912 feet * 12 inches/foot = approximately 22.94 inches
Therefore, the approximate length of the desk in the drawing is 22.94 inches.
Looking at the answer choices, the closest value is 22.94 inches:
d. 2 7/10