SOLUTION: Hi I need if anyone could help me with this prob.. 1. A carpet is to cover 2/3 of the floor area of a room 20m by 30m. The uncovered part of the floor is to form a strip of un

Question 657350: Hi I need if anyone could help me with this prob..
1. A carpet is to cover 2/3 of the floor area of a room 20m by 30m. The uncovered part of the floor is to form a strip of uniform width around the carpet. Find the dimensions of the carpet.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A carpet is to cover 2/3 of the floor area of a room 20m by 30m.
The uncovered part of the floor is to form a strip of uniform width around the carpet.
Find the dimensions of the carpet.
:
Find the area of the room; 20 * 30 = 600 sq/m
Find the 2/3 of that area; * 600 = 400 sq/m is the area of the carpet
:
Let x = the width of of strip around the carpet
Then the dimensions of the carpet will be (20-2x) by (30-2x)
:
using the area of the carpet, find x
(20-2x)*(30-2x) = 400
FOIL
600 - 40x - 60x + 4x^2 = 400
Arrange as a quadratic equation
4x^2 - 100x + 600 - 400 = 0
4x^2 - 100x + 200 = 0
simplify, divide by 4
x^2 - 25x + 50 = 0
This will not factor, use the quadratic formula; a=1; b=-25; c=50
Two solutions but only x ~ 2.2 m, will make sense
:
find the dimensions of the carpet
20 - 2(2.2) = 15.6 m
30 - 2(2.2) = 25.6 m
:
Check this by finding the area with these dimensions:
15.6 * 25.6 = 399.36 ~ 400 sq/m
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