The perimeter of a rectangular field is 1400m and the ratio of the sides is 3:4. Find the area of the field

Question

Plz help me solve

Answer 1

Let's say that the rectangle has length of x and width of y. That means the perimeter is 2x + 2y = 1400. 

 

We also know that the ratio of the width to the length is 3:4 which means y/x = 3/4.

 

This is now a system of equations with 2 equations and 2 unknowns.

 

To solve, we start by rearranging the second equation giving us y = 3x/4.

 

We then replace all the y in the first equation by substituting the second equation into the first one wherever we see y:

 

2x + 2(3x/4) = 1400

 

This gives us an equation with only x as the unknown which we can solve:

 

2x + 2(3x/4) = 2x + 3x/2 = 3.5x = 1400

 

x = 1400/3.5 = 400 <- this is the length. 

 

Since we know that x = 400, we can now substitute this value back into the second equation to solve for y:

 

y = 3x/4 = 3(400)/4 = 300. 

 

The field's dimensions are 300m x 400m.