The lenght of a rectangular room is twice its width if the diagonal of this room measures 6.7m?

Question

what are the dimensions of the room?

Answer 1

You're given L = 2W. You also know that L^2 + W^2 = D^2 from the Pythagorean Theorem. So substituting the first equation into the second you have 4W^2 + W^2 = D^2: 5W^2 = D^2. D^2 = 6.7^2 = 44.89, so 5W^2 = 44.89. Divide by 5: W^2 = 8.97. I think we can round that to 9, given that if it were 9, the diagonal would still be rounded to 6.7. So say that W^2 = 9, then W = 3. The room is 3 m wide, and since it's twice as long as it is wide, it's 6 m long.

Answer 2

28 feet x 59 feet Right, let's imagine there is no "3 foot longer", so the length is just twice as long as the width. This would mean that 3 x the length of the long side is equal to the perimeter(because the two widths are equal to one long length). However, we were forgetting about the 3 foot. Because there are two sides that are 3 foot longer than twice the width that is 6 foot altogether. Take 6 from 174 = 168. Because of the bit that we have already established (without 3 foot the perimeter is three times the length of the long side) we can now, pretending that the perimeter is 168 foot determine that 168(perimeter) / 3 = length of long side. It equals 56. Now comes putting it all together. 56 is equal to the length of the long side without the extra 3 foot which equals twice the length of the width. Therefore, the width equals 28. The length of the long side is twice this and add 3 which equals 59. I've checked it and it works. THIS WAS HARD! DON'T LISTEN TO THOSE WHO SAY 42 AND 45. THEY FORGOT ABOUT THE "TWICE THE WIDTH" BIT AND JUST DID "THREE FEET LONGER"!!!

Answer 3

Let the width of the room be x and its length 2x
Therefore (x)^2+(2x)^2 = 5x^2 is the square of its diagonal
So,the digonal isxsqrt5
According to the problem.
x(sqrt)5=6.7m
=>x=6.7/sqrt5=3m
the width of the room is 3 m and the length is 6m

Answer 4

Pythagorean theorem says

6.7^2 = L^2 + W^2
= (2W)^2 + W^2
= 4W^2 + W^2
= 5W^2

So W^2 = 6.7^2 / 5 = 9, and W = 3, L = 6.

Answer 5

L^2 + W^2 = (6.7)^2
L=2W
so (2W)^2 + W^2 = 44.89
W=Sqrt(44.89/5)= 2.996331=3.0(correct to 2 sig fig)
L=6.0(correct to 2 sig fig)
the dimension of this room is 3.0m by 6.0m

Answer 6

L=2W
D=6.7
(D ) power 2 = (L ) power 2 + ( W ) power 2
(6.7) power 2 = (2w )power 2 + (w) power 2
44.89=4w squ.+w squ.
44.89=5w squ.
w= squ. root of 44.89/5
w=.......

L=2w

Answer 7

let length=2x
breadth=x

so, (2x)^2 +(x)^2 =(6.7)^2
or 5x^2 = 44.89
or x^2 = 8.978
or x = 2.99
hence breadth =2.99 m
lengh = 5.98 m

Answer 8

d^2=l^2+w^2=5w^2
d=w*sqrt(5)
6.7=w*sqrt(5)
w=6.7/sqrt(5)=3
l=6

the room is 3m*6m