The diagonal of a square has a length of 9 square root over two ft. what is the length of the square?

There are two way to solve this: 1) since a square with a diagonal forms a 45,45,90 triangle there a special relationship to the length of the sides and the diagonal lengths with a 45-45-90 right angle triangle a) the two side have the same exact length b) the diagonal Length is the Length of one of the side times square root 2 so a square with a diagonal length of 9 sq rt 2 ft as a side of 9 ft you can use the Prythmation formula C^2 = A^2+B^2 (9 sqrt( 2))^2 = A^2 + B^2 - since B = A so (9 sqrt( 2))^2 = 2 (A^2) (12.727922061357855439215198517887)^2 = 2( A^2) 162 = 2 A^2 162 * 1/2 = A^2 162/2 = A ^2 81 = A^2 sq rt(81) = sqrt(A^2 ) 9 = A again it the same answer as the above .

since it is a square, all sides are the same length. And since the diagonal is 9square root 2, u have got urself a right-angled triangle with two legs same length and the hypotenous is 9suqare root2, u use pythagoras theoram. Pythagoas theoram is a^2 + b^2 = c^2 so assuming that one side of a square is"x", u would have x^2 + x^2 =(9root2)^2 2x^2 = 9^2 times (root2)^2 2x^2 = 81 times 2 2x^2 = 162 x^2 = 162/2 x^2 = 81 x = square root of 81 x = 9 the length of the square is 9ft. theres ur answer, enjoy!!!!!!!!!

I don't get what you mean by 9 square root over two ft. Do you mean the square root of 9 over two? That is 3/2 or 1 and 1/2. If I could understand it, I could solve it. I guess you meant 9 times the square root of 2. In that case (9sq rt of 2) squared = 2 x^2 and x =9 , so each side is 9.

2x^2 = (9sqrt(2))/2)^2 x = 4.5. The 2x^2 represents the two equal sides formed by the right triangle that consists of these two sides and the diagonal, and the squared is because I used the pythagorean theorem (that is also why the right hand side is squared).

it's a special right triangle problem, (45, 45, 90) both sides are x, and the hypotenuse is sqrt(2)x so... if your hypotenuse is 9sqrt(2), then x=9 ......9 ..._____ ...|....../.| 9 |.../....| 9 ...|/____| ...... 9 the diagonal is 9sqrt(2)

c^2 = a^2 + b^2 c = 9sqrt2/2 a = b (9sqrt2/2)^2 = 2a^2 81 * 2/4 = 2a^2 divide both side by 2 (81 * 2)/(4*2) = a^2 81/4 = a^2 a = 9/2 a = 4.5

9 to the seoncnd power --------------------------------------… two feet th anser is 4.5

ratio of 1:1:sqrt2 and you have 9sqrt2 in place of sqrt 2 so other sides must be 9 by 9 ft.(did you mean 9 times sqrt of 2 rather than 9sqrt over 2???)

I don't get what you mean by 9 square root over two ft. Do you mean the square root of 9 over two? That is 3/2 or 1 and 1/2. If I could understand it, I could solve it. I guess you meant 9 times the square root of 2. In that case (9sq rt of 2) squared = 2 x^2 and x =9 , so each side is 9.