Question

A rectangle has a diagonal length of 5cm and one side with length 3cm. Find the area of the rectangle.

Answer 1

Answer:

   Area of the rectangle is $12cm^2$

Step-by-step explanation:

Given:

Diagonal= 5 cm

Length=3 cm

The diagonal of a rectangle cuts it into two equal Right triangles, where the length of the third side can be found by using the Pythagorean theorem i.e:

$Hypotenuse^2=Perpendicular^2+Base^2$

The diagonal is the hypotenuse of the triangle as its the longest side of the triangle formed:

$Diagonal^2=Length^2+Width^2$

$5^2=3^2+Width^2$

$25=9+width^2$

$width^2=25-9$

$width^2=16$

$Width=\sqrt{16}$

$Width=4 cm$

Area of a rectangle= $length*Width$

                             $= 3cm * 4cm\\\\Area=12cm^2$

Area of the rectangle is $12cm^2$