Question

An old manuscript reveals that a landowner in the time of King Arthur held 3.00 acres of land plus livestock area of 25.0 perches by 4.00 perches. What was the total area in the unit of roods?

Answer 1

Roods and acre are units of area used since olden times. We are given information about 2 areas, one in acres another in perches square. We need to convert acres to roods and square perches to roods.

Complete answer:
In the hierarchy of units, acre is the bigger unit, a rood is smaller than an acre and a perch is smaller than a rood.
Rule for conversion:
An acre contains 4 roods and a rood contains 40 (square) perches.
We divide the question in two parts for the given area. In the first part, we would convert the acre land into roods and in the second part; we first obtain the land area from the given dimensions and make a conversion of the obtained area from square perches to roods.
1. Landowner held 3 acres of land so in roods, he has
$3 \times 4 = 12$roods.
2. The livestock land has a dimension of 25 perches by 4 perches. The area for this land becomes,
$25 \times 4 = 100 perch^2$.
Now, 1 rood has 40 square perches. This means that 1 square perch is equal to $\dfrac{1}{40}$ roods. So, the livestock land in roods is given by:
$100 perch^2 = \dfrac{100}{400}roods = 2.5 roods$.
The total land that the landowner held, now becomes 12 roods + 2.5 roods = 14.5 roods.

Note:
For the first land, the area of the land was given while for the second livestock land, the dimension of the land was given instead. So we have used, simply, the formula for finding the area of a rectangle i.e., length into breadth to find the area for the second land.