Question

a farmer divides a rectangular piece of land with a perimeter of 140 yards into two triangular parts as shown in the diagram. if the area of abc is 600 square yards, what is the area of acd?
a. 880 square yards
b. 740 square yards
c. 600 square yards
d. 460 square yards

Explanation:

Step1: Recall the property of triangles in a rectangle

In a rectangle \(ABCD\), \(\triangle ABC\) and \(\triangle ACD\) have the same base and height.
The area of a triangle is given by \(A=\frac{1}{2}\times base\times height\).
For \(\triangle ABC\), \(A_{ABC}=\frac{1}{2}\times AB\times BC = 600\) square yards.
For \(\triangle ACD\), \(A_{ACD}=\frac{1}{2}\times AD\times DC\).
Since \(AB = DC\) and \(BC=AD\) (properties of a rectangle).

Step2: Conclude the relationship between the areas

The formula for the area of \(\triangle ABC=\frac{1}{2}\times length\times width\) and the formula for the area of \(\triangle ACD=\frac{1}{2}\times length\times width\) (where \(length\) and \(width\) are the sides of the rectangle).
So, \(A_{ACD}=A_{ABC}\)

Answer:

C. 600 square yards