Question

Two triangles have the same base lengths. One Triangle has the height that is 4 times the height of the other triangle. Are the heights and the areas of the two triangles proportional?

Answer 1

YES

• Area of Triangle 1

Base=b

Height= h

Area 1=A1=1/2*b*h

• Area of Triangle 2

Base=b

Height= 4h

Area of triangle 2=A2=1/2*b*4h

• Comparing A1 and A2

A2/A1= (1/2*b*4h)/(1/2*b*h)

= (1/2*b*4h)/(1/2*b*h)

=4/1

Ratio of heights =h2/h1= 4/1

Ratio of areas =A2/A1= 4/1

They are proportional.