The floor of james’s living room is 12 feet by 18 feet.What is the area,in square feet,of the largest circular rug that can fit
in James’s living room?
2 answers:
Hi there!
Since we're trying to find a circular rug in a rectangular room room, we'll use a diagram like the image attached. As you can see, the circle uses the width of the room for its diameter. Since the room is 12 by 18, 12 would be the diameter of the circle since it is also the width of the room. Now, we need to find the area of the circle with a diameter of 12 feet. The radius would be 6 feet because the radius is always half of the diameter. The formula for the area of a circle is A = pi x r^2. All we need to do is to plug in the numbers to find the area of the circle. Plugging in the numbers, we get A = pi x 36. (36 is 6 squared) Therefore, the largest circular rug that can fit in James' living room is 36pi ft^2 or 113.1ft^2.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Since we're trying to find a circular rug in a rectangular room room, we'll use a diagram like the image attached. As you can see, the circle uses the width of the room for its diameter. Since the room is 12 by 18, 12 would be the diameter of the circle since it is also the width of the room. Now, we need to find the area of the circle with a diameter of 12 feet. The radius would be 6 feet because the radius is always half of the diameter. The formula for the area of a circle is A = pi x r^2. All we need to do is to plug in the numbers to find the area of the circle. Plugging in the numbers, we get A = pi x 36. (36 is 6 squared) Therefore, the largest circular rug that can fit in James' living room is 36pi ft^2 or 113.1ft^2.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
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Answer:
For the first one
x= About 32.02
y= About 27.58
z= About 55.16
For the second one
x= 6
y= 12
z= about 16.97
Step-by-step explanation:
Their all really simple
These are special right triangles, a 45, 45, 90 and a 30, 60, 90 triangle. The formla for these triangles are shown in the picture below.
Now for the first one ]
Lets find Z first
Now this is a 45 special right triangle so we know the other side s 39 but the hypotenuse is n (I’m using N becuase x and y is taken) So n is basically 39 (look at the image below) and just solve that. Now for x and y. We know its a 30, special right triangle. We know that 39 here is already the answer for N
so make an equation to find the n and you’ll get 27.58 for y. Now For x, its just doubled the y.
For the second one this is easier
We know that the x is (6) becuase its already in the radical number, now to find the hypotnuse, we double that and get 12. Now we know what y is becuase since the 2nd triangle is a 45/45/90, we know that 12 is y, the hypotnuse is just N and we just plug in the n with 12 and solve it!
