A rectangle has a length of 4 feet and a perimeter of 14 feet. what is the perimeter of a similar rectangle with a width of 9 feet?a. 36 ftb. 108 ftc. 42 ftd. 126 ft
Accepted Solution
A:
First Rectangle: P= 14; L= 4, W= ? Second Rectangle: P= ?, L= ?, W= 9
STEP 1: solve for the width in the first rectangle using perimeter formula
Perimeter= 2L + 2W 14= 2(4) + 2W
14= 8 + 2W subtract 8 from both sides
6= 2W divide both sides by 2
3= W
STEP 2: Since the two rectangles are similar, they may be different sizes, but they have corresponding angles. We can set up a ratio to compare width and length.
First Rectangle: P= 14, L= 4, W= 3 Second Rectangle: L= ?, W= 9
length/width= length/width 4/3= L/9
cross multiply 4 * 9= 3 * L
36= 3L divide both sides by 3
12= L
STEP 3: find perimeter of second rectangle; use length from step 2