MATH SOLVE

4 months ago

Q:
# 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

Perimeter= 2L + 2W

=2(12) + 2(9)

=24 + 18

=42 feet

ANSWER: (C) 42 feet

Hope this helps! :)

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

Perimeter= 2L + 2W

=2(12) + 2(9)

=24 + 18

=42 feet

ANSWER: (C) 42 feet

Hope this helps! :)