If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 meters squared, what is the length of each of the shorter sides?

This needs to be found by substitution and then by factoring. First we know that, using the perimeter formula for a rectangle, the perimeter is 46=2L+2W and the area is 76=L*W. We need to solve for one of those variables cuz we have too many unknowns right now. Let's solve the perimeter formula for L: 46=2L+2W, 2L=46-2W and L=23-W. Now that we have a value for L in terms of W, sub that L value in to the area formula to solve for W: 76=L*W, 76=(23-W), 76=23W-W^2, and W^2-23W+76=0. We have to factor that now to solve for the 2 values of W. When we factor that, we get that W=19 and W=4. Let's first try out the W value of 19 in our L substitution formula: L=23-W so L=23-19 and L=4. That means that we have a Width of 19 and a Length of 4. Trying out the other W of 4 we get L=23-W so L=23-4 and L=19. That gives us a Width of 4 and a Length of 19. In both cases we have a combination of 4 and 19. So whether we say that the length is shorter than the width or that the width is shorter than the length doesn't matter because we only have 2 values for both and they want the shorter of the 2 sides in number not definition. In other words they don't want you to decide if width is shorter or longer than length, they only want the number value for the shorter side which is 4. That's your 4

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