The correct options are (a) and (d). Both (a) and (d) are possible base and height values for the second triangle with the same area.
If the area of the triangles remains constant, then the product of the base and height for each triangle should be the same.
For the first triangle:
Area_1 = 1/2 × base_1 × height_1
= 1/2 ×base_1 ×height_1
= 1/2 ×12m×8m
=48m^2
Now, for the second triangle, let the base be b_2 and the height be h_2
We know that the area of the second triangle is also 48 m².
Area_2 = 1/ 2 ×b_2 ×h_2
48= 1/2 ×b_2 ×h_2
Now, we can find the possible values for b_2 and h_2 from the given options:
a) b_2 =120 and h_2 =80
1/2 ×120×80=48m^2
b) b_2 =10 and h_2 =10
1/2 ×10×10=25m^2
c) b_2 =60 and h^2 =36
1/2 ×60×36=1080m^2
d) b_2 =16 and h_2= 6
1/2 ×16×6=48m^2
So, the correct options are (a) and (d). Both (a) and (d) are possible base and height values for the second triangle with the same area.
Question
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 12 m and its height is 8 m?
a) 120 m and 80 m
b) 10 m and 10 m
c) 60 m and 36 m
d) 16 m and 6 m.