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3 years ago

9. The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm2,

Mathematics

1 answer:

makvit [3.9K]3 years ago

5 0

Answer:

length: 13 cm

width: 5 cm

Step-by-step explanation:

You may be aware that 65 = 5×13. We note that 13 is 3 more than twice 5, so these are the dimensions of the rectangle:

5 cm wide; 13 cm long

If you want so solve this algebraically, you can let w represent the width. Then the length is 2w+3 and the area is ...

A = LW

65 = (2w+3)(w)

In standard form, this equation is ...

2w^2 +3w -65 = 0

To factor this, you look for factors of 2×(-65) = -130 that have a sum of 3. Those would be ...

-130 = (-10)(13)

Then the factored equation is ...

2w^2 +13w -10w -65 = 0

w(2w+13) -5(2w+13) = 0

(w -5)(2w +13) = 0 ⇒ w = 5, -13/2

The positive solution makes sense in this problem, so ...

width = 5 cm

length = 2(5) +3 = 13 cm

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3 years ago

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vredina [299]

составим уравнение
11х=9х+124
2х=124
х=62

проверим ответ
682=558+124

тогда, общее количество детей

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2 years ago