Question

a gardenner is designing a new garden in the shape of a trapezoing she wants the short base to be twice the height and loger base to be 4 feet longer than the shorter base if she has enough top soild create a 60ft2 garden what dimensions should be use for the garden?

Answer 1

Height = 5 ft

Short base = 10 ft

Long base = 14 ft

Explanation:

Let h = height, a = short base, b = long base.

From the question,

a = 2h

b = a + 4 = 2h + 4

The area of the trapezoid is given by
`(1)/(2)(a+b)h`. Thus,

`60 = (1)/(2)(2h + 2h + 4)h`

`60 = ((4h + 4)h )/(2)`

`60 = (4h(h + 1))/(2)`

`60 = 2h(h + 1)`

`30 = h(h + 1)`

`0 = h^2 + h - 30`

`0 = (h+6)(h-5)`

`h-5 = 0` or
`h+6 = 0`

`h= 5` or
`h = -6`

We discard the negative value of h since it is a measurement and cannot be negative.

`h= 5`

`a= 2h=2*5=10`

`b= a+4=10+4=14`