Question

n of the horse training center shows its measurements in meters. lin and noah each rent expression to find the area of the training center. y 20 40 yard arena sion: area of yard area of arena length of center width of center be lins expression. s exprssion. yard + area of arena ? ?

Explanation:

Step1: Calculate the area of the yard

The area of a rectangle is calculated by the formula \(A = length\times width\). For the yard, the length is \(y\) and the width is \(40\), so the area of the yard is \(40y\).

Step2: Calculate the area of the arena

For the arena, the length is \(20\) and the width is \(40\), so the area of the arena is \(40\times20 = 800\).

Step3: Calculate the total area using Lin's method

Lin's method is to add the area of the yard and the area of the arena. So the expression is \(40y + 800\).

Step4: Calculate the total area using Noah's method

Noah's method is to use the formula for the area of a rectangle where the total length is \((y + 20)\) and the width is \(40\). Using the formula \(A=(y + 20)\times40=40y+800\) (by distributive property \(a(b + c)=ab+ac\), here \(a = 40\), \(b=y\), \(c = 20\)).

Answer:

Lin's expression: \(40y+800\) (area of yard \(40y\) + area of arena \(800\)). Noah's expression: \(40(y + 20)\) (length of center \((y + 20)\times\) width of center \(40\)).