• Purpose: To solve word problems that involve area.

• Homework: Finish teaching worksheet. Pg. 173 1-6 all.

Example #1

• A rectangle is 3 times long as it is wide. If the length is increased by 6 and the width by 8, the area is increased by 108. Find the original dimensions.

• You may want to draw the rectangles first.

• 3x 3x + 6

• x x + 8

Example #1 (cont.)

• You know from the problem that when you increase the dimensions the area is also so set up the equation like this:

• Original Area + Increase = New Area

• 3x(x) + 108 = (3x + 6)(x + 8) FOIL

• 3x² + 108 = 3x² + 30x + 48 3x² CANCEL

• 108 = 30x + 48 Subtract 48

• 60 = 30x x = 2 Original was 2 x 6

Example #2

• A painting is 10 in. longer than is wide and is bordered by a 3 in. frame on all sides. If the area of the frame alone is 402 in.², what are the dimensions of the painting.

• Draw a diagram to help you.

• By putting a frame

• all around you add 6

• to the L and W

Example #2 (cont.)

• Area of Picture + Frame = Total Area

• x(x + 10) + 402 = (x + 6)(x + 16) FOIL

• x² + 10x + 402 = x² + 22x + 96 x² CANCEL

• 10x + 402 = 22x + 96 Subtract 10x

• 402 = 12x + 96 Subtract 96

• 306 = 12x Divide by 12

• 25.5 = x so W = 25.5 and L = 35.5