A. A right triangle with base 48 inches and height 2 inches.
B. A right triangle with base 32 inches and height 3 inches.
C. A right triangle with base 12 inches and height 4 inches.
D. A right triangle with base 16 inches and height 6 inches.
E. A right triangle with base 24 inches and height 24 inches.
F. A right triangle with base 96 inches and height 1 inch.
Answer:
A, B, D, F
Step-by-step explanation:
The area of any triangle is the product of its base and height:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a triangle}}\\\\A=\dfrac{1}{2}bh\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{$A$ is the area.}\\ \phantom{ww}\bullet\;\textsf{$b$ is the base.}\\ \phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
Substitute A = 48 into the area formula to determine the product of the base and height of a triangle with an area of 48 square inches:
[tex]\dfrac{1}{2}bh=48\\\\\\2\cdot \dfrac{1}{2}bh =2\cdot 48\\\\\\bh=96[/tex]
Therefore, the product of the base and height of a triangle with an area of 48 square inches is 96 square inches.
Now, identify the factors pairs of 96:
Any triangle with an area of 48 square inches can have a factor pair of 96 as their base and height. Therefore, the given triangles that have an area of 48 square inches are:
