29.8k views
5 votes
9. The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm2,

find its length and the width.

User Leemour
by
8.0k points

1 Answer

3 votes

Answer:

length: 13 cm

width: 5 cm

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

User Matt Accola
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories