Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
I believe you multiple 343 times a hundred and the answer you gt you divide it by 35 and then you get 980?
This would be about 13 cm
The three numbers are 12, 18 and 24
Arithmetic progression
Let the 3 number in arithmetic progression be:
a-d, d, a+d ...
If their sum is 3, then;
a-d+d+a+d = 3
2a + d = 3 ........... 1
If the sum of their squares is 11, then;
(a-d)² + d² + (a+d)² = 11
a²-2ad+d²+d²+a²+2ad+d² 11
2a²+3d² = 11 ....... 2
Solving the equations simultaneously, d = 6 and a = 12
First-term = 12
second term = 18
Thirs term = 24
Hence the three numbers are 12, 18 and 24
Hope this helps you!!!!!! :D
