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bezimeni [28]
3 years ago
13

the length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions

Mathematics
1 answer:
KIM [24]3 years ago
6 0
Let
x---------> the length of the rectangle
y--------> the width of the rectangle

we know that
A=84 ft²
[area of rectangle]=x*y-----> 84=x*y-----> equation 1
x=y-5------> equation 2
substitute 2 in 1
84=[y-5]*y-----> 84=y²-5y---------> y²-5y-84=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=12
x=y-5-----> x=12-5-----> x=7

the answer is
the length of the rectangle is 7 ft
the width of the rectangle is 12 ft

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The answers are complex numbers...

Here's why...

---------

p+q=18

pq=82

---------

Therefore:

p=18-q

p=82/q

------------

Therefore:

18-q=82/q

q(18-q)=q(82/q)

18q-q²=82

(-1)(18q-q²)=82(-1)

q²-18q=-82

(q-9)²-9²=-82

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(q-9)²=-82+81

(q-9)²=-1

q-9=-√(-1)=-i

q-9=√(-1)=i

-----------

Therefore:

q=9-i

q=9+i

-------------

ANSWERS:

When q=9-i, p=9+i

When q=9+i, p=9-i

-----------

Proof:

p+(9-i)=18

p+9-i=18

p=18-9+i

p=9+i

....

p+(9+i)=18

p+9+i=18

p=18-9-i

p=9-i

--------------

More proofs:

p=82/(9+i)

p=(82/(9+i))*((9-i)/(9-i))

p=(82(9-i))/(81-9i+9i-i²)

p=(82(9-i))/(81-(-1))

p=(82(9-i))/82

p=9-i

---------------

p=82/(9-i)

p=(82/(9-i))*((9+i)/(9+i))

p=(82(9+i))/(81+9i-9i-i²)

p=(82(9+i))/(81-(-1))

p=(82(9+i))/82

p=9+i
3 0
2 years ago
Read 2 more answers
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