Question

The Doe family had a rectangular garden with a 58-foot perimeter. They reduced the length by 7 feet and decreased the width to be half as wide as it was originally. This resulted in a garden with a 34-foot perimeter. What is the area of the new smaller garden?

Answer 1

Answer:

60 square foot

Step-by-step explanation:

Perimeter of a rectangular garden = 58 foot

Let x and y denote length and width of the rectangular garden.

2 (Length + Width) = Perimeter of the rectangular garden

$2(x+y)=58\\x+y=\frac{58}{2}\\ x+y=29$

So,

length = x

width = y = $29-x$

The length is reduced by 7 feet and the width becomes half.

New length = $x-7$

New width = $\frac{1}{2}(29-x)$

New perimeter = 34 foot

$2[(x-7)+\frac{1}{2}(29-x)]=34\\ 2[2(x-7)+(29-x)]=2(34)\\2(x-7)+(29-x)=34\\2x-14+29-x=34\\2x-x-14+29=34\\x+15=34\\x=34-15\\x=19$

So,

New length $=x-7=19-7=12\,\,foot$

New width = $\frac{1}{2}(29-19)=\frac{1}{2}(10)=5\,\,foot$

Area of the new smaller garden = New length × New Width

= 12 × 5

= 60 square foot