Question

a rectangular mat has a perimeter of 52 inches. drag numbers to the lines to complete the expression that shows the area of the rectangle in terms of its width, w, in inches. area = _ w² + _ w + ___ -52 -26 -13 -1 0 1 13 26 52

Explanation:

Step1: Find the length in terms of width

The perimeter formula for a rectangle is \(P = 2(l + w)\). Given \(P=52\), we have \(52 = 2(l + w)\). Dividing both sides by 2 gives \(l + w=26\), so \(l = 26 - w\).

Step2: Calculate the area

The area formula for a rectangle is \(A=l\times w\). Substitute \(l = 26 - w\) into the area formula: \(A=(26 - w)\times w\).
Using the distributive property \(a(b - c)=ab - ac\) (here \(a = w\), \(b = 26\), \(c = w\)), we get \(A=26w-w^{2}\).
Rewriting in the form \(Ax^{2}+Bx + C\), we have \(A=-w^{2}+26w+0\)

Answer:

\(-1\), \(26\), \(0\)