4. The length to the floor is 32m longer than its width and there
is greater than 200 square meters you will cover the floor completely with tiles. What will be the possible dimension of the floor?
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Answer:
L , B length & width of floor
floor area = ( w+32)*w =200
w^2 +32w -200 =0
w = -32+ or - sqrt of ( 32 ^2 - 4*1* (-200)) /2
= -32 + or - sqrt of( 1024+800) /2
= -32 + or - sqrt of(1824) /2
= (-32 + or - 42.71) / 2 = 10.71 /2
= 5 .355 m
L = 5 .355 m +32 = 37 .355 m
Dimensions of the floors are L by W = 37 .355 m by 5 .355m
Hope this is helpful for you.
Step-by-step explanation:
Length = l
Width = w
Area = w * l
Given is that area is more than 200, and that l = w + 32
200 = w * l = w * (w + 32) = w² + 32w
w² + 32w - 200 = 0
Using quadratic equation method we find w = -16 + 2√114 or -16 - 2√114
Only the first has a positive value.
So possible dimensions are any dimensions where
l = w + 32 and w > -16 + 2√114 (or w > 5.354)
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