Can someone please help me with this A maths question?

Question

The area of a rectangle is [12+ (30 over square root 3)] m2. Given that the length is m, find, without the use of a calculator, find the perimeter of the rectangle.

The length is (3+ square root 12) m

Answer 1

The length is m and the width is an unknown w. The area is equal to length times width, or mw, but we've also been told that the area is [12 + (30 / sqrt(3)]m^2, and I assume you mean m as in the length rather than meters. So we set the two expressions for area equal to each other.

[12 + (30 / sqrt(3)]m^2 = mw ==> w = [12 + (30 / sqrt(3)]m

The perimeter is just twice the sum of length and width, or 2m + 2w = 2m + 2*[12 + (30 / sqrt(3)]m = m(14 + 10*sqrt(3)).

If m^2 in the area referred to square meters, then maybe the length was also given in meters, as in "Given that the length is 5 m," rather than just "m" as you typed. In that case, you would still set the two expressions equal to each other, except that m^2 would not be part of the given expression, and the other expression would be 5w (if the length were 5 m).

Answer 2

hi, you need to be more specific in the equation you gave.

is m2 = square of m ; or
m * 2

"30 over square root 3" = 30/(square root of 3)?

My interpretation of your equation is as follows:

area = [ 12 + 30/(square root of 3)] * (m square)

You can solve the question using the following simultaneous equations:

let m = length and b = breadth
area = m * b
perimeter = 2*m + 2*b

m * b = [ 12 + 30/(square root of 3)] * (m square)
(cancel both side of m)

b = [ 12 + 30 / (square root of 3)] * m

therefore,

perimeter
= 2*m + 2 {[12+30/(square root of 3)]*m}
= 2m + 24 + 60m/(square root of 3)
= 24 + 2m [1 + 30/(square root of 3)]

Answer 3

Does m2 mean m times m = m^2? If so ... then ...

The area is times m^2
The length is m, so the width must be times m
The perimeter is m + m + m + m

The = [12 + 30 / sqrt(3) ]

Answer 4

Length (L) = (3+ SQRT(12)) = 3 + 2SQRT(3)
Width = W
Perimeter = 2L + 2W
Area (A) = 12 + 30/SQRT(3) = L*W ...... W = A/L
Perimeter = 2A/L + 2L = 2(A + L^2)/L

Perimeter = 2(12+ 30/SQRT(3)) + (3 + 2SQRT(3))^2)/ (3 + 2SQRT(3))

P = 2(12 + 30/SQRT(3) + 9 + 12SQRT(3) + 4(3))/ (3 + 2SQRT(3))

P = 2(33 + 30/SQRT(3) + 12SQRT(3))/(3 + 2SQRT(3))
P = 2(33SQRT(3) + 30 + 12(3))/[SQRT(3)(3 + 2SQRT(3))]
P = 2(33SQRT(3) + 66)/(3SQRT(3) + 6)
P = 22(3SQRT(3) + 6)/(3SQRT(3) + 6)
P = 22

The perimeter is 11

Answer 5

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Answer 6

something is missing about the traingle to solve your problem. Just knowing the area is not sufficiient to solve your problem, we need other info to know the perimeter.