Need help with GCSE Maths question

An answer or guidance would be greatly appreciated.

perimeter of rectangle = 20
lets take x and y as sides of the rectangle
perimeter = 2(x+y)
20 = 2(x+y)
10 = x+y
X= 10-y (1)
area of rectangle = area of equilateral triangle ( in this question)
area of rectangle = xy
area of equilateral triangle = root3/4 * asquared ( in this case a is 2x)
area of eq... triangle = root3/4 * 4xsquared

xy = root3/4 * 4xsquared
dividing both sides by x
y= root3/4 * 4x
we know x= 10-y
y= root3/4 * 40-4y
5y= 10root3
y= 2root3
x= 10-2root3
perimeter of equi... triangle = 3a ( a = 2x)
perimeter = 6x
= 6( 10 - 2root3)
= 39.2 cm ( 1dp)
the method is correct but might have done some calculation error. ( is this the right answer??)

Thanks for the help but I thought you couldn't add 4y to both sides if you are multiplying root3/4 by (40-4y)?

perimeter of rectangle = 20
lets take x and y as sides of the rectangle
perimeter = 2(x+y)
20 = 2(x+y)
10 = x+y
X= 10-y (1)
area of rectangle = area of equilateral triangle ( in this question)
area of rectangle = xy
area of equilateral triangle = root3/4 * asquared ( in this case a is 2x)
area of eq... triangle = root3/4 * 4xsquared

xy = root3/4 * 4xsquared
dividing both sides by x
y= root3/4 * 4x
we know x= 10-y
y= root3/4 * 40-4y
5y= 10root3
y= 2root3
x= 10-2root3
perimeter of equi... triangle = 3a ( a = 2x)
perimeter = 6x
= 6( 10 - 2root3)
= 39.2 cm ( 1dp)
the method is correct but might have done some calculation error. ( is this the right answer??)

Please do not post full maths solutions you are only supposed to give hints as the rules state in the maths forum

Is this calculator or non calculator?

your right!! you add root3y to both sides (root3/4*4y= root3y)

Here's a tip:

The height of an equilateral triangle is $\frac{\sqrt{3}}{2}$ times the length of the triangle.

$\Rightarrow$ length of the rectangle is $\sqrt{3}$ times the width.