A rectangular patio has an area of 20 5/6 ft^2, and the width is 3 1/2 feet. What is the length of the patio.

Question

A rectangular patio has an area of 20 5/6 ft ^2, and the width is 3 1/2 feet.  What is the length of the patio?

Answer 1

Here's what we know:

area of a rectangle: a = l * w

a = 20 ⁵/₆

w = 3 ¹/₂

So:

20 ⁵/₆ = l * 3 ¹/₂

 

To isolate l, we need to divide both sides by 3 ¹/₂ But before that, it might be helpful to convert the integer parts into their fractions:

¹²⁵/₆ / ⁷/₂

That turns into:

¹²⁵/₆ * ²/₇

 

That gives us:

²⁵⁰/₄₂

Simplified:

¹²⁵/₂₁

21 goes into 125 five times:

5 ²⁰/₂₁

So our length is 5 ²⁰/₂₁