Two diagonals of a square are expressed as 4x-7 feet and 2x+11 feet. Find the perimeter of the square.

Question

-Needs to be rounded to the tenths place.

Answer 1

since the two diagonals have the same length, you can set 4x-7 = 2x+11 and solve for x, and thus you will know the diagonal length.  from that, divide by square root of two, to determine side length; the perimeter is then four times that side length.

Answer 2

the diagonals of a square are equal in length

4x-7=2x+11

4x-2x=11+7

2x=18

x=9

each diagonal is 4*9-7=29 feet or 2*9+11=29 feet

a diagonal of a square forms two right isosceles triangles, two 45-45-90 right triangles

the hypotenuse is always equal to the length of a side times √2

let s=length of any one of the sides

29=s√2

square both sides

841=2s²

s²=841/2

s=√(841/2)

s=29/√2

s=29√2/2 feet  (you can find this by using the Pythagorean Theorem also)

P=4s is the formula for the perimeter of a square

P=4*(29√2/2)

P=2*29√2

P=58√2

P=58*1.414213

P=82.024354

P=82.0 feet rounded to tenths

You can eliminate the "square both sides" steps.