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ZanzabumX [31]
4 years ago
7

The height of a trapezoid is 8 in. And its area is 96 in2. One base of the trapezoid is 6 inches longer than the other base. Wha

t are the lengths of the bases? Complete the explanation of how you found your answer. One base is Use the formula for the area of a trapezoid. Substitute 96 for A and 8 for h and simplify the equation to find = (b1 + b2). Use guess and check to find two numbers that add to with one number 6 more than the other to get
Mathematics
1 answer:
Vsevolod [243]4 years ago
5 0

Answer:

The lengths of the bases are 9 inches and 15 inches.

Step-by-step explanation:

The area of trapezoid is

=\frac12(\textrm{ sum of parallel sides})\times height

Given that the height of a trapezoid is 8 in. and its area is 96 in².

Assume the bases of the trapezoid be b₁ and b₂.

Since one base of the trapezoid 6 in. longer than the other.

Let, b₁=b₂+6

The area of the trapezoid is

=\frac 12 (b_1+b_2)\times8 in²

=\frac12 (b_2+6+b_2)\times 8 in²

=\frac12(2b_2+6)\times8 in²

According to the problem,

\frac12(2b_2+6)\times8 =96

\Rightarrow 2b_2+6=\frac{96\times 2}{8}                [ Multiplying \frac28 ]

\Rightarrow 2b_2+6=24

\Rightarrow 2b_2=24-6

\Rightarrow 2b_2=18

\Rightarrow b_2=\frac{18}{2}

\Rightarrow b_2=9

Then, b_1=b_2+6

              =9+6

             =15 in

The lengths of the bases are 9 inches and 15 inches.

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