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The area of a shape is the amount of space it can occupy.
The number of isosceles triangle in the grid is: [tex]\mathbf{\frac{2x^2}{u^2}}[/tex]
The dimension of the grid is given as:
[tex]\mathbf{Dimension = x\ by\ x}[/tex]
Calculate the area
[tex]\mathbf{A_1 = x\ \times \ x}[/tex]
[tex]\mathbf{A_1 = x^2}[/tex]
The area of each isosceles triangle is given as:
[tex]\mathbf{A_2 = \frac 12u^2}[/tex]
The number (n) of the triangle in an x-by-x grid is:
[tex]\mathbf{n = A_1 \div A_2}[/tex]
So, we have:
[tex]\mathbf{n = x^2 \div \frac 12u^2}[/tex]
Express as products
[tex]\mathbf{n = x^2 \times \frac{2}{u^2}}[/tex]
[tex]\mathbf{n = \frac{2x^2}{u^2}}[/tex]
Hence, the number of isosceles triangle in the grid is: [tex]\mathbf{\frac{2x^2}{u^2}}[/tex]
Read more about areas at:
https://brainly.com/question/16418397