Question

A, B and C are points on the line 2x+y=8

DCE is a straight line.
AB:BC=2:1
EC:DC=1:2

Work out the ratio Area of triangle AEC : Area of triangle BCD

Give your answer in its simplest form.

Answer 1

The ratio of the area of triangle AEC and area of triangle BCD is 21:14 if the A, B and C are points on the line 2x+y=8

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have line;

2x+y=8

x/4 + y/8 = 1

Coordinate for A(4, 0) and B(0, 8)

To find the coordinate C we will use external section formula:

Let (a, c) be a coordinate for C

AB : BC = 2:1

AC:BC = 3:1  

$\rm C(a, b) =( \dfrac{-4}{3-1}, \ \dfrac{24}{3-1})$

C(a, b) = (-2, 12)

Let coordinate for E(0, e) and for D(f, 0)

EC:DC=1:2 and C(-2, 12)

So after applying section formula, we will get:

E(0, -3) and D(0, 36)

Area of triangle AEC = (1/2)(7)(12) = 42 square units

Area of triangle BCD = (1/2)(28)(2) = 28 square units

ratio of area of triangle AEC : area of triangle BCD = 42:28

= 21:14

Thus, the ratio of the area of triangle AEC and area of triangle BCD is 21:14 if the A, B and C are points on the line 2x+y=8

Learn more about the linear equation here:

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