Answer:
(a) LM=12 units, LN=35 units, MN=37 units
(b)8 84 units
(c) 210 square units
Step-by-step explanation:
(a)
Since points L and M have same x coordinates, it means they are in the same plane. Also, since the Y coordinates of L and N are same, they also lie in the same plane
Length ![LM=\sqrt {(7-7)^{2}+(16-4)^{2}}=12 units](https://tex.z-dn.net/?f=LM%3D%5Csqrt%20%7B%287-7%29%5E%7B2%7D%2B%2816-4%29%5E%7B2%7D%7D%3D12%20units)
Length ![LN=\sqrt {(42-7)^{2}+(4-4)^{2}}=35 units](https://tex.z-dn.net/?f=LN%3D%5Csqrt%20%7B%2842-7%29%5E%7B2%7D%2B%284-4%29%5E%7B2%7D%7D%3D35%20units)
Length![MN=\sqrt {(42-7)^{2}+(4-16)^{2}}=37 units](https://tex.z-dn.net/?f=MN%3D%5Csqrt%20%7B%2842-7%29%5E%7B2%7D%2B%284-16%29%5E%7B2%7D%7D%3D37%20units)
Alternatively, since this is a right angle triangle, length MN is found using Pythagoras theorem where
![MN=\sqrt {(LN)^{2}+(LM)^{2}}=\sqrt {(12)^{2}+(35)^{2}}=37 units](https://tex.z-dn.net/?f=MN%3D%5Csqrt%20%7B%28LN%29%5E%7B2%7D%2B%28LM%29%5E%7B2%7D%7D%3D%5Csqrt%20%7B%2812%29%5E%7B2%7D%2B%2835%29%5E%7B2%7D%7D%3D37%20units)
Therefore, the lengths LM=12 units, LN=35 units and MN=37 units
(b)
Perimeter is the distance all round the figure
P=LM+LN+MN=12 units+35 units+37 units=84 units
(c)
Area of a triangle is given by 0.5bh where b is base and h is height, in this case, b is LN=35 units and h=LM which is 12 units
Therefore, A=0.5*12*35= 210 square units
Then, Owen only uses one piece of the 4 yard ropes.
Answer:
![60\ ft^{2}](https://tex.z-dn.net/?f=60%5C%20ft%5E%7B2%7D)
Step-by-step explanation:
we know that
The area of the carpet needed is equal to the area of the complete rectangle minus the area of the two triangles
so
![A=(12)(6)-\frac{1}{2}(4)(4)-\frac{1}{2}(4)(2)=72-8-4=60\ ft^{2}](https://tex.z-dn.net/?f=A%3D%2812%29%286%29-%5Cfrac%7B1%7D%7B2%7D%284%29%284%29-%5Cfrac%7B1%7D%7B2%7D%284%29%282%29%3D72-8-4%3D60%5C%20ft%5E%7B2%7D)