The length of a rectangle garden is 4 meters more than its width. The area of the rectangle is 60 meters. What's the dimensions of the rectangle?

Answer 1

Hello, Myah,

Let L be the length and W the width. We are told that L =W + 4. We also know the area is equal to W*L, which is 60 m² (I assume the 60 meters is meant to be 60 square meters)

Use the first definition of L in the area equation:

A=W*L

A=W(W+4)

60 = W² +4W

W² +4W - 60 = 0

We can factor this into (W - 6)(W + 10)

That nmakes the roots W=6 and W=-10. -10 m² makes no sense for our 3D world, but W = 6 does.

The dimensions are thus:

W = 6m², and

L = 10m²

WL = 60m²

Bob

Answer 2

Hey Myah,

The length for this rectangle is 10 and the width is 6.

Let's first set length= L and width = W.

From the given details, we know that the Area = 60 and L=W+4 (length of a rectangle garden is 4 meters more than its width).

Recall the formula for the rectangle area is Area = Width * Length, which is 60 = W* L. We also know that L = W+4. Replacing L with (W+4), we can set up an equation that 60 = W(W+4), and expand it to W^2+4W-60=0

From here, you can either use the graphing calculator to find the zero or use the quadratic formula to solve the equation. I used the quadratic formula for demonstration purposes, and the answer turned out to be W=(-4±16)/2, where W = 6, -10. Because it is impossible to have a negative value for the real-life applications, so we omit W= -10.

Therefore the answer for width is 6, and plug it back into L=W+4, you will get the length is 10.