SOLUTION: The circumference of a rectangle with sides a and b is 100 cm. If a is shortened by 5 cm and lengthened b by 6 cm, the surface area is reduced by 60 cm2. Calculate the lengths of

Algebra ->  Surface-area -> SOLUTION: The circumference of a rectangle with sides a and b is 100 cm. If a is shortened by 5 cm and lengthened b by 6 cm, the surface area is reduced by 60 cm2. Calculate the lengths of       Log On


   

Question 1070052: The circumference of a rectangle with sides a and b is 100 cm. If a is shortened by 5 cm and lengthened b by 6 cm, the surface area is reduced by 60 cm2.
Calculate the lengths of sides a and b.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
A circumference of a rectangle is called "the perimeter" and is NEVER called "a circumference of a rectangle".

Also, rectangle HAS NO "surface area". It has "the area", in opposite and/or instead.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That should be "perimeter" of the rectangle.

a%2Bb%2Ba%2Bb=100
2a%2B2b=100
a%2Bb=50

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%28a-5%29%28b%2B6%29, this area is reduced by 60 cm-squared.
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ab-%28a-5%29%28b%2B6%29=60
%2850-b%29b-%2850-b-5%29%28b%2B6%29=60, substituted for a;
50b-b%5E2-%2845-b%29%28b%2B6%29=60
50b-b%5E2-%2845b-b%5E2%2B45%2A6-6b%29=60
50b-b%5E2-45b%2Bb%5E2-45%2A6%2B6b=60
50b-45b%2B6b-b%5E2%2Bb%5E2-270=60
11b-270=60
11b=60%2B270
11b=330
b=%2833%2A10%29%2F11
highlight%28b=30%29

Finding a:
a%2Bb=50
a=50-b
a=50-30
highlight%28a=20%29