SOLUTION: The length of a rectangle is 3 less than 5 times of its width. write a simplified algebraic expression for the perimeter of a rectangle. if the rectangle width is tripled and its

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Question 957614: The length of a rectangle is 3 less than 5 times of its width.
write a simplified algebraic expression for the perimeter of a rectangle.
if the rectangle width is tripled and its length is doubled the perimeter of new rectangle is 92 cm greater than original perimeter.
Find the area of the original rectangle.
PLZZZ explain how u solved this?
and fast plz!!!!
Found 3 solutions by josgarithmetic, macston, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Length, L, width w.
The length of a rectangle is 3 less than 5 times of its width.
L=-3%2B5w.

p, perimeter of the rectangle.
p=2L%2B2w
p=2%285w-3%29%2B2w
p=10w-6%2B2w
highlight_green%28p=12w-6%29



if the rectangle width is tripled and its length is doubled the perimeter of new rectangle is 92 cm greater than original perimeter.

Now the dimensions are changed to width 3w and length 2%285w-3%29=10w-6. The new perimeter is given as 12w-6%2B92.

The question is, find the area of the original rectangle, but you need to solve for w, and then for L so that the area can be calculated. Return to the perimeter formula for using with the new perimeter situation.

p=2%2AnewLength%2B2%2AnewWidth
12w-6%2B92=2%2810w-6%29%2B2%283w%29, with the expressions substituted.
12w%2B86=10w-12%2B6w
86=4w-12
4w=92
highlight%28w=23%29----------Use the given formula for L to find value of L.

L=5w-3
L=5%2A23-3
highlight%28L=112%29

Original rectangle's area, highlight%28w%2AL=23%2A112=highlight%282576%29%29.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=width; L=length=5W-3; P=perimeter
Original rectangle:
P=2(L+W) Substitute for L
P=2((5W-3)+W)=6W-3=12W-6
Original perimeter is 12W-6
New rectangle:
W%5Bn%5D=3W; L%5Bn%5D=2L=10W-6
=2%2813W-6%29=26W-12
New perimeter is 26W-12
New perimeter-original perimeter=92 cm
P%5Bn%5D-P=92cm
%2826W-12%29-%2812W-6%29=92cm
14W-6=92cm
14W=98cm
W=7cm The original width was 7cm.
L=5W-3=5(7cm)-3=35cm-3cm=32cm The original length was 32cm.
Area=L*W=32cm*7cm=224 sq cm
ANSWER: The area of the original rectangle is 224 square centimeters.
CHECK
New Perimeter-Original Perimeter=92cm
2(2L+3W)-2(L+W)=92cm
2(64cm+21cm)-2(32cm+7cm)=92cm
2(85cm)+2(39cm)=92cm
170cm-78cm=92cm
92cm=92cm















Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The length of a rectangle is 3 less than 5 times of its width.
write a simplified algebraic expression for the perimeter of a rectangle.
if the rectangle width is tripled and its length is doubled the perimeter of new rectangle is 92 cm greater than original perimeter.
Find the area of the original rectangle.
PLZZZ explain how u solved this?
and fast plz!!!!
Area of original rectangle: highlight_green%28224%29cm%5E2