Question

perimeter & area of use the polygon tool to draw a rectangle with a perimeter of 28 units and an area of 40 square units. start drawing at the vertex shown. polygon undo redo reset

Explanation:

Step1: Recall rectangle formulas

For a rectangle with length \( l \) and width \( w \), perimeter \( P = 2(l + w) \) and area \( A = lw \). Given \( P = 28 \) and \( A = 40 \).
From perimeter: \( 2(l + w)=28 \Rightarrow l + w = 14 \). From area: \( lw = 40 \).

Step2: Solve for \( l \) and \( w \)

We need two numbers that add to 14 and multiply to 40. Solve the system: \( l + w = 14 \), \( lw = 40 \). The quadratic equation: \( x^2 - 14x + 40 = 0 \). Factoring: \( (x - 10)(x - 4)=0 \). So \( l = 10 \), \( w = 4 \) (or vice versa).

Step3: Draw the rectangle

Start at the given vertex. Move 10 units right (length) and 4 units down (width), then complete the rectangle (or 4 right and 10 down, depending on grid orientation). On the grid, from the black dot, move horizontally 10 units (or 4) and vertically 4 units (or 10) to form the rectangle.

Answer:

To draw the rectangle, from the starting vertex, move 10 units horizontally and 4 units vertically (or 4 units horizontally and 10 units vertically) to form the rectangle with length 10 and width 4 (perimeter \( 2(10 + 4)=28 \), area \( 10\times4 = 40 \)).