Question

The area of a trapezoid is found with the formula A=1/2(b1+b2)h
.

A trapezoidal banner has an area of 120 m² and a height of 10 m. Base 1 (b1)
is 16 m shorter than base 2 (b2)
. What are the lengths of the two bases? Let b represent the length of base 1.

Answer 1

To find the lengths of the two bases of the trapezoidal banner, we can start by using the formula for the area of a trapezoid:

\[
A = \frac{1}{2}(b_1 + b_2)h
\]

We are given the area \( A = 120 \, \text{m}^2 \) and the height \( h = 10 \, \text{m} \). We can plug these values into the formula:

\[
120 = \frac{1}{2}(b_1 + b_2) \cdot 10
\]

This simplifies to:

\[
120 = 5(b_1 + b_2)
\]

Now, divide both sides by 5:

\[
b_1 + b_2 = 24 \quad (1)
\]

Next, we know that base 1 \( b_1 \) is 16 m shorter than base 2 \( b_2 \). We can express this relationship as:

\[
b_1 = b_2 - 16 \quad (2)
\]

Now, we can substitute equation (2) into equation (1):

\[
(b_2 - 16) + b_2 = 24
\]

Combine like terms:

\[
2b_2 - 16 = 24
\]

Add 16 to both sides:

\[
2b_2 = 40
\]

Now, divide by 2:

\[
b_2 = 20 \quad (base \, 2)
\]

Now, we can find \( b_1 \) using equation (2):

\[
b_1 = b_2 - 16 = 20 - 16 = 4 \quad (base \, 1)
\]

Thus, the lengths of the two bases are:

- Base 1 (\( b_1 \)) = 4 m
- Base 2 (\( b_2 \)) = 20 m