Answer:
The length is 15 yards
Step-by-step explanation:
Given
Represent the width with W and length with L: So
![Area = 135yd^2](https://tex.z-dn.net/?f=Area%20%3D%20135yd%5E2)
![L=3W - 12](https://tex.z-dn.net/?f=L%3D3W%20-%2012)
Required
Determine the length of the rectangle:
Area is calculated as thus:
![Area = L * W](https://tex.z-dn.net/?f=Area%20%3D%20L%20%2A%20W)
Substitute 3W - 12 for L and 135 for Area
![135= (3W - 12) * W](https://tex.z-dn.net/?f=135%3D%20%283W%20-%2012%29%20%2A%20W)
![135= 3W^2 - 12W](https://tex.z-dn.net/?f=135%3D%203W%5E2%20-%2012W)
Reorder:
![3W^2 - 12W - 135= 0](https://tex.z-dn.net/?f=3W%5E2%20-%2012W%20-%20135%3D%200)
Divide through by 3
![W^2 - 4W - 45 = 0](https://tex.z-dn.net/?f=W%5E2%20-%204W%20-%2045%20%3D%200)
Expand:
![W^2 - 9W + 5W - 45 = 0](https://tex.z-dn.net/?f=W%5E2%20%20-%209W%20%2B%205W%20-%2045%20%3D%200)
![W(W - 9) + 5(W - 9) = 0](https://tex.z-dn.net/?f=W%28W%20%20-%209%29%20%2B%205%28W%20-%209%29%20%3D%200)
![(W + 5)(W-9) = 0](https://tex.z-dn.net/?f=%28W%20%2B%205%29%28W-9%29%20%3D%200)
or ![W - 9 = 0](https://tex.z-dn.net/?f=W%20-%209%20%3D%200)
or ![W = 9](https://tex.z-dn.net/?f=W%20%3D%209)
But width can't be negative
So:
![W = 9](https://tex.z-dn.net/?f=W%20%3D%209)
Recall that: ![L=3W - 12](https://tex.z-dn.net/?f=L%3D3W%20-%2012)
![L = 3 * 9 - 12](https://tex.z-dn.net/?f=L%20%3D%203%20%2A%209%20-%2012)
![L = 15](https://tex.z-dn.net/?f=L%20%3D%2015)
<em>Hence, the length 15 yards</em>
The drawing shows a circle, with the two lines forming a cross assumed to be perpendicular to each other, so this is most likely to be a square, as the four points at which the perpendicular lines intersect with the circle can be connected to form a square.
We would need 3 points for an equilateral triangle, 5 for a pentagon, and 6 for a hexagon, which do not fit the current steps.
Answer:
-0.17157287525
Step-by-step explanation:
1. The square root of 8 will never be a whole number so it is 2.82842712475
2. Square root of 9 is 3.
3. You can already realize that the answer will not be whole or positive
4. Subtract in order.
5. The answer is -0.17157287525
Answer:
Step-by-step explanation:
The total surface area of the sphere = 2πr²
Total surface area of the cylinder = 2πr²+2πrh
Total surface area of the solid = 4πr²+2πrh
r is the radius of the sphere and the cylinder
h is the height of the cylinder
Total surface area of the solid = 2πr(r+h)
If the total height of the solid is 18 cm, then r+h = 18cm
Given the Total surface area of the solid = 205π cm
205π = 2πr(r+h)
205π = 2πr(18)
205π = 36πr
205 = 36r
Divide both sides by 36
205/36 = 36r/36
r = 5.69cm
Since r+h = 18cm
5.69+h = 18
h = 18-5.69
h = 12.31cm
By pythagorean theorem
a^2+b^2=c^2
We can find that PL is 12.65
and then by altitude theorem
MA*LA=PA^2
we can find the value of MA
12MA=16
MA=1.33
then by the pythagorean theorem
we can use to find PM
MA^2+PA^2=PM^2
so PM=4.22
then to find the are you multiply length by width
PM*PL
12.65*4.22
So the area is 53.38