find the area of a rectangle of length 4cm and whose diagonal is 8cm leave your answer in surd form​

The area of rectangle is: 16√3 cm^2Step-by-step explanation:The given information forms two right angled triangles (Picture Attached)HereBase = AB = 4cmHypotenuse = BD = 8cmWe have to find the length of perpendicular which will be the width of the rectangle[tex]BD^2 = AB^2 + AC^2\\(8)^2 = (4)^2 + AC^2\\64 = 16 + AC^2\\AC^2 = 64 -16\\AC^2 = 48\\Taking\ square\ root\ on\ both\ sides\\\sqrt{AC^2} = \sqrt{48}\\AC = \sqrt{16*3}\\AC = 4\sqrt{3}[/tex]The width is:[tex]4\sqrt{3}[/tex]Area = Length * Width[tex]= 4 * 4\sqrt{3}\\=16\sqrt{3}\ cm^2[/tex]The area of rectangle is: 16√3 cm^2Keywords: rectangle, AreaLearn more about area at:brainly.com/question/10703930brainly.com/question/10772025#LearnwithBrainly