The expression [tex]2ab+c^2[/tex] represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
the equivalent expression [tex]a^2+b^2+2ab[/tex]use the length of the figure to represent the area
[tex]2ab+c^2=a^2+b^2+2ab\\subtract \; 2ab \; from \; both \; sides\\c^2=a^2+b^2[/tex]
Given :
Figure of a square with some shaded triangles.
Area of the triangle formula is 1/2 times base times height
base =a and height =a
Area of one triangle =[tex]\frac{1}{2} ab[/tex]
There are 4 shaded triangles
Area of 4 shaded triangles =[tex]4 \cdot \frac{1}{2} ab=2ab[/tex]
Area of the square = side times side
Area of the white square with side 'c' =[tex]c \cdot c= c^2[/tex]
The expression [tex]2ab+c^2[/tex] represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
Now we find the area of outer square . side length is a+b
Area of outside square =[tex](a+b)(a+b)=(a+b)^2=a^2+b^2+2ab[/tex]
the equivalent expression [tex]a^2+b^2+2ab[/tex]use the length of the figure to represent the area
Now set both the areas equal to each other
[tex]2ab+c^2=a^2+b^2+2ab\\subtract \; 2ab \; from \; both \; sides\\c^2=a^2+b^2[/tex]
Learn more : brainly.com/question/20605745
