Pregunta
Sam has a patio that is in the shape of a rectangle with an area of
will be a larger rectangle. The current patio has a length of 30 ft and a wi
new width 3 times the current width.
(a) Fill in the blanks to describe the size of Sam’s new patio.
New length
(b) How will the expansion change the area of the patio?
The area of the new patio will be
times the area of the curre
© Sam’s friend Lisa also wants to expand her rectangular patio. Li
current patio. She goes to Sam for advice. Fill in the blank so th
Make the new length 7 times the current length, and make the
(tt
will be a larger rectangle. The current patio has a length of 30 ft and a wi
new width 3 times the current width.
(a) Fill in the blanks to describe the size of Sam’s new patio.
New length
(b) How will the expansion change the area of the patio?
The area of the new patio will be
© Sam’s friend Lisa also wants to expand her rectangular patio. Li
current patio. She goes to Sam for advice. Fill in the blank so th
Make the new length 7 times the current length, and make the
(tt
Ask by Bates Flynn. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(a) New Length: 30 ft, New Width: 60 ft
(b) The area of the new patio will be 3 times the current area.
© The area of Lisa’s new patio will be 7 times her current patio area.
(b) The area of the new patio will be 3 times the current area.
© The area of Lisa’s new patio will be 7 times her current patio area.
Solución
Let’s break down the problem step by step.
Known Conditions:
- Current patio area:
- Current length of the patio:
- Current width of the patio:
can be calculated using the area formula .
Step 1: Calculate the Current Width
Using the area formula:
To find
:
Step 2: Determine the New Dimensions of Sam’s Patio
(a) The new width is 3 times the current width:
The new length remains the same as the current length:
So, the new dimensions of Sam’s patio are:
- New Length:
- New Width:
Step 3: Calculate the Area of the New Patio
The area of the new patio can be calculated as:
Let’s calculate this area:
(b) To find how the expansion changes the area of the patio:
Step 4: Advice for Lisa’s Patio Expansion
© Lisa wants to make her new length 7 times the current length and make the new width the same as the current width.
Let’s denote Lisa’s current length as
and current width as
. The new dimensions will be:
- New Length:
- New Width:
The area of Lisa’s new patio will be:
Thus, the area of Lisa’s new patio will be
times the area of her current patio.
Summary of Answers:
(a) New Length:
, New Width:
(b) The area of the new patio will be times the area of the current patio.
© The area of Lisa’s new patio will be times the area of her current patio.
(b) The area of the new patio will be
© The area of Lisa’s new patio will be
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Extra Insights
Sam’s current patio has a length of 30 ft and a width of 20 ft, as
. With a new width that is 3 times the current width, that makes it
ft. Thus, Sam’s new patio will have a length of 30 ft and a width of 60 ft, which leads to a new area of
square feet, making it
times the area of the current patio.
Lisa can take a leaf out of Sam’s book! If she decides to make her new length
times her current length and doubles the width of her existing patio, she can simply apply the same area expansion principles. If her current area is
, her new area formula would be
, leading to a
times increase in area! That’s what I call growing your patio and your potential!
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