Question

A rectangular shaped garden is 2 feet longer than the width. If its area is 143sq. feet, find the dimensions.

Answer 1

width = 11

lenght = 13

Step-by-step explanation:

The area (A) of a tringle is:

A = wl

where

A = area

w = width

l = lenght

In this exercise, we know that:

A = 143 feet²

w = x

l = x + 2

We can substitute this values in the general formula and find the value of x:

A = wl

143 = (x)(x + 2)

143 = x² + 2x

x² + 2x - 143 = 0

Now we have a quadratic equation and we can solve it using the Quadratic formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{\Delta}}{2a}\text{ ; }\Delta=b^2-4ac \\ In\text{ this exercise:} \\ \Delta=2^2-4\cdot1\cdot(-143) \\ \Delta=4+572 \\ \Delta=576 \\ x=\frac{-2\pm\sqrt[]{576}}{2\cdot1} \\ x=(-2\pm24)/(2) \\ x=(22)/(2)=11 \\ or \\ x=-(26)/(2)=-13 \end{gathered}`

Since we can not have a negative value for x, x = 11

w = 11

l = 13