Answer:
9 inches and 15 inches
Step-by-step explanation:
The height of a trapezoid is 4 in.
Its area is 48 in^2.
Let a be one base and b be the second base.
One base is 6 inches longer than the other. This implies that:
a = 6 + b _________ (1)
The formula for the area of a trapezoid is given as:
[tex]A = \frac{1}{2}(a + b)h[/tex]
where h = height
From (1), we have that:
[tex]A = \frac{1}{2}(6 + b + b )h\\ \\A = \frac{1}{2}(6 + 2b )h[/tex]
We have that h = 4 and A = 48 in^2, therefore:
[tex]48 = \frac {1}{2}(6 + 2b) * 4\\ \\96 = 24 + 8b\\\\8b = 96 - 24 = 72\\\\b = 72 / 8 = 9 in[/tex]
=> a = 6 + 9 = 15 in
The bases are 9 inches and 15 inches long.
