Question

Which of the following right triangles have an area of 48 square inches? Select three that apply. 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 1

A. A right triangle with base 48 inches and height 2 inches.

• area = 1/2bh
• area = 1/2*48in*2in
• area = 48 in^2 , yes

B. A right triangle with base 32 inches and height 3 inches.

• area = 1/2bh
• area = 1/2*32in*3in
• area = 48 in^2 ,yes

C. A right triangle with base 12 inches and height 4 inches.

• area = 1/2bh
• area = 1/2*12in*4in
• area = 24 in^2 ,no

D. A right triangle with base 16 inches and height 6 inches.

• area = 1/2bh
• area = 1/2*16in*6in
• area = 48 in^2, yes

E. A right triangle with base 24 inches and height 24 inches.

• area = 1/2bh
• area = 1/2*24in*24in
• area = 288 in^2 ,no

F. A right triangle with base 96 inches and height 1 inch.

• area = 1/2bh
• area = 1/2*96in*1in
• area = 48 in^2,yes

Answer 2

Answer:

A, B, D, F

Step-by-step explanation:

The area of any triangle is the product of its base and height:

$\boxed{\begin{array}{l}\underline{\textsf{Area of a triangle}}\\\\A=\dfrac{1}{2}bh\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{ A is the area.}\\ \phantom{ww}\bullet\;\textsf{ b is the base.}\\ \phantom{ww}\bullet\;\textsf{ h is the height.}\end{array}}$

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:

$\dfrac{1}{2}bh=48\\\\\\2\cdot \dfrac{1}{2}bh =2\cdot 48\\\\\\bh=96$

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:

• 1 and 96
• 2 and 48
• 3 and 32
• 4 and 24
• 6 and 16
• 8 and 12

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:

• A. A right triangle with base 48 inches and height 2 inches.
• B. A right triangle with base 32 inches and height 3 inches.
• D. A right triangle with base 16 inches and height 6 inches.
• F. A right triangle with base 96 inches and height 1 inch.