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

Answer:

Height = 5 ft

Short base = 10 ft

Long base = 14 ft

Step-by-step 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 $\frac{1}{2}(a+b)h$. Thus,

$60 = \frac{1}{2}(2h + 2h + 4)h$

$60 = \frac{(4h + 4)h }{2}$

$60 = \frac{4h(h + 1)}{2}$

$60 = 2h(h + 1)$

$30 = h(h + 1)$

$0 = h^2 + h - 30$

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

$h-5 = 0$ 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.

$h= 5$

$a= 2h=2\times5=10$

$b= a+4=10+4=14$