Certainly! Let's analyze each statement in detail to determine whether it’s true or false based on geometric principles.
### Statement A:
"If you know the area and length of a rectangle, you can find its width."
- True. In a rectangle, the area [tex]\( A \)[/tex] is given by the product of its length [tex]\( l \)[/tex] and width [tex]\( w \)[/tex]:
[tex]\[
A = l \times w
\][/tex]
Therefore, if you know the area and the length, you can rearrange the formula to solve for the width:
[tex]\[
w = \frac{A}{l}
\][/tex]
So, this statement is True.
### Statement B:
"To find the height of a trapezoid, you can divide its area by half of the sum of its bases."
- True. The area [tex]\( A \)[/tex] of a trapezoid is given by:
[tex]\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\][/tex]
where [tex]\( b_1 \)[/tex] and [tex]\( b_2 \)[/tex] are the lengths of the two bases, and [tex]\( h \)[/tex] is the height. Rearranging to solve for height [tex]\( h \)[/tex]:
[tex]\[
h = \frac{A}{\frac{1}{2} \times (b_1 + b_2)} = \frac{2A}{b_1 + b_2}
\][/tex]
This matches the statement, so it is True.
### Statement C:
"To find the base length of a triangle, you can divide the area of the triangle by its height and then multiply by 2."
- True. The area [tex]\( A \)[/tex] of a triangle is given by:
[tex]\[
A = \frac{1}{2} \times b \times h
\][/tex]
where [tex]\( b \)[/tex] is the base and [tex]\( h \)[/tex] is the height. To solve for the base [tex]\( b \)[/tex]:
[tex]\[
b = \frac{2A}{h}
\][/tex]
This confirms the statement, so it is True.
### Statement D:
"To find the height of a parallelogram, you can multiply its area by its base length."
- False. The area [tex]\( A \)[/tex] of a parallelogram is given by:
[tex]\[
A = b \times h
\][/tex]
where [tex]\( b \)[/tex] is the base length and [tex]\( h \)[/tex] is the height. To solve for height [tex]\( h \)[/tex]:
[tex]\[
h = \frac{A}{b}
\][/tex]
Multiplying the area by the base length isn’t correct; instead, you should divide the area by the base length. Therefore, this statement is False.
### Conclusion:
- Statement A: True
- Statement B: True
- Statement C: True
- Statement D: False
So, all the statements have been analyzed and your answers should be marked accordingly.
