Finding the Relation of the Areas in Two Similar Right Triangles

Question

The question is as follows:

Right triangle A has base b, height h, and area x. Right triangle B has length $2b$ and width $2h$. What is the area of rectangle B in terms of x?

I tried to substitute in values for b and h to find the area x.

$b = 4$ and $h = 2$, therefore, $x = 4$.

$2b = 8$ and $2h = 4$, therefore, area would be $16$.

This shows that the area is 4 times greater in Right Triangle B.

However, the correct answer is actually that the area is 8 times greater. I do not know why. Any help will be appreciated.

Answer 1

Area of right triangle

$$Area_{right\, triangleA}= \frac12\cdot b\cdot h= x $$

Area of rectangle

$$Area_{rectangle}= b\cdot h= 2x $$

Area of rectangle scaled double length and width.

$$A_{rectangleB}= 2b\cdot 2h= 4bh= 8x. $$

Answer 2

It asks for the area of the rectangle $B$, so if $B$ has base = $2b$ and height = $2h$, then the area of the rectangle $B$ is $4bh$. The area of triangle $A$ is $\frac{1}{2} bh$. Thus, rectangle $B$ has an area 8 times greater than triangle $A$