Each diagonal of a rectangle measures 5 cm and its width is 3square root cm. Find the lenght of the rectangle?

Answer 1

The square root of 22.

It uses the pythagoream theorem. When you split the rectangle with the diagonals it becomes two triangles. short side squared + long side squared = diagonal squared. So you square the diagonal and subtract the width squared. Then you take the square root of that answer because it's equal to that side squared.

Answer 2

Using the Pythgorean Theorum for right triangles is the easiest way to deal with this one. A rectangle is made up of two right triangles. The diagonal is one side of each triangle, the width and length make up the other two sides for each triangle. The Pythagorean Theorum states A squared plus B squared equals C squared where A and be are the two sides and C is the hypotenuse (the longest side). In this case we have A is the width, B is the length and C is the diagonal. Rearranging it to solve for B results in: C squared minus A squared equals B squared. Substituting the known values gives us 5 squared minus (square root of 3) squared = B squared or 25 minus 3 equals B squared. Further solving gives us 22 equals B squared so the length is equal to the square root of 22.

Answer 3

If the diagonal of the rectangle is 5 and one leg is 3, then you may use the pythagorean theorem on this and say (5 squared) = (sqrt 3 squared) + (x squared)...so 25=3+(x squared) therefore the length would be the square root of 22

Answer 4

Take one of the diagonals as the hypotenuse of a triangle; then the height would be sqr[3] cm. So by our old friend Pythagoreus,
l^2 + (sqr[3])^2 = 5^2, or
l^2 = 25-3 = 22
Length of a side, l = sqr[22]

Answer 5

Draw out the picture and see what's missing...look at the definition of a rectangle & see what you'd use to fill in the missing piece.

Answer 6

do your own homework