Question

A rectangular garden has an area of 131.25 square feet. If the length is 10 feet longer than the width, what are the dimensions of the garden?

Answer 1

Width=7.5 ft

Length=17.5 ft

Explanation:

-Let w be the width's dimension.

-Therefore Length=w+10

-The area is given as 131.25 sq ft.

-We substitute in the area formula to solve for w:

`Area=Length* Width\\\\131.25=w(w+10)\\\\131.25=w^2+10w\\\\\#Equate \ to \ 0\\\\w^2+10w-131.25=0\\\\100w^2+1000w-13125=0\\\\w_1,w_2=(-b\pm√(b^2-4ac))/(2a)\\\\w_1,w_2=(-1000\pm √(1000^2-4*100*(-13125))/(2*100)\\\\w_1=7.5, w_2=-17.5\\\\\therefore w=w_1=7.5\ ft\\\\length=w+10=7.5+10=17.5\ ft`

Hence, the length of the rectangle is 17.5 ft and the width is 7.5 ft