Answer:
200ft^2
Step-by-step explanation:
From the first sentence;
L = 2B
Perimeter of a rectangle = 60ft
P = 2[ L +B ]
substitute as follows;
60 = 2( 2B + B)
60 = 2(3B)
60 = 6B
B = 10ft
To find L
L = 2B
L = 2*10
L = 20 ft
Area of a rectangle = LB
= 20×10
=200ft^2
Answer
Given the statement: In parallelogram ABCD, diagonals AC and BD intersects at point E.
Given that ABCD is a parallelogram.
As, we know that in a parallelogram diagonals bisect each other.
Since AC and BD intersect at E, and we get E is the mid point of both diagonals AC and BD.
⇒ BE = DE .....[1]
Substitute the given values of
and
in [1] we have;
![2x^2-3x = x^2+10](https://tex.z-dn.net/?f=2x%5E2-3x%20%3D%20x%5E2%2B10)
Subtract
on both sides we get;
![2x^2-3x-x^2 = x^2+10-x^2](https://tex.z-dn.net/?f=2x%5E2-3x-x%5E2%20%3D%20x%5E2%2B10-x%5E2)
Simplify:
![x^2-3x =10](https://tex.z-dn.net/?f=x%5E2-3x%20%3D10)
Subtract 10 on both sides we get;
![x^2-3x-10 =0](https://tex.z-dn.net/?f=x%5E2-3x-10%20%3D0)
or
![x^2-5x+2x-10 =0](https://tex.z-dn.net/?f=x%5E2-5x%2B2x-10%20%3D0)
![x(x-5)+2(x-5)=0](https://tex.z-dn.net/?f=x%28x-5%29%2B2%28x-5%29%3D0)
![(x-5)(x+2)=0](https://tex.z-dn.net/?f=%28x-5%29%28x%2B2%29%3D0)
equate these factors equal to zero we get;
(x-5) = 0 and (x+2) = 0
we have;
x = 5 and x = -2
Since, x cannot be negative.
So, x =5
![BE = DE = x^2+10 = (5)^2+10 = 25+10 = 35 units](https://tex.z-dn.net/?f=BE%20%3D%20DE%20%3D%20x%5E2%2B10%20%3D%20%285%29%5E2%2B10%20%3D%2025%2B10%20%3D%2035%20units)
Diagonals BD = BE + DE = 35 + 35 =70 units.
Therefore, the value of BD = 70 units.
Answer: Weight of Charles = 177.5 pounds
Weight of dos = 22.5 pounds.
Step-by-step explanation:
Let x = Weight of Charles
y = Weight of dog.
As per given , we have the following system of linear equation :
![x+y=200--------(i)\\\\x-20=7y-----------(ii)](https://tex.z-dn.net/?f=x%2By%3D200--------%28i%29%5C%5C%5C%5Cx-20%3D7y-----------%28ii%29)
We can write (ii) as :
![x-7y=20---(iii)](https://tex.z-dn.net/?f=x-7y%3D20---%28iii%29)
Subtract equation (iii) from (i) , we get
![8y=180\\\\ y=\dfrac{180}{8}=22.5](https://tex.z-dn.net/?f=8y%3D180%5C%5C%5C%5C%20y%3D%5Cdfrac%7B180%7D%7B8%7D%3D22.5)
Put this value in (1) , we get
![x+22.5=200\Rightarrow\ x=200-22.5=177.5](https://tex.z-dn.net/?f=x%2B22.5%3D200%5CRightarrow%5C%20x%3D200-22.5%3D177.5)
Hence , Weight of Charles = 177.5 pounds
Weight of dos = 22.5 pounds.
6x+15=27
6x/6=12/6
X=2
27-15=12