Question

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

Answer 1

The area of rectangle is: 16√3 cm^2

Step-by-step explanation:

The given information forms two right angled triangles (Picture Attached)

Here

Base = AB = 4cm

Hypotenuse = BD = 8cm

We have to find the length of perpendicular which will be the width of the rectangle

$BD^2 = AB^2 + AC^2\\(8)^2 = (4)^2 + AC^2\\64 = 16 + AC^2\\AC^2 = 64 -16\\AC^2 = 48\\Taking\ square\ root\ on\ both\ sides\\\sqrt{AC^2} = \sqrt{48}\\AC = \sqrt{16*3}\\AC = 4\sqrt{3}$

The width is:

$4\sqrt{3}$

Area = Length * Width

$= 4 * 4\sqrt{3}\\=16\sqrt{3}\ cm^2$

The area of rectangle is: 16√3 cm^2

Keywords: rectangle, Area

Learn more about area at:

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