Answer:
Area of the rectangle is [tex]12cm^2[/tex]
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:
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
The diagonal is the hypotenuse of the triangle as its the longest side of the triangle formed:
[tex]Diagonal^2=Length^2+Width^2\\[/tex]
[tex]5^2=3^2+Width^2[/tex]
[tex]25=9+width^2[/tex]
[tex]width^2=25-9[/tex]
[tex]width^2=16[/tex]
[tex]Width=\sqrt{16} \\[/tex]
[tex]Width=4 cm[/tex]
Area of a rectangle= [tex]length*Width[/tex]
[tex]= 3cm * 4cm\\\\Area=12cm^2[/tex]
Area of the rectangle is [tex]12cm^2[/tex]
