# Finding the Relation of the Areas in Two Similar Right Triangles

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.

• Is $B$ a triangle or a rectangle? That's a factor of $2$ right there. – lulu Jul 12 '18 at 18:11
• Even if $b$ is a hypotenuse of right triangle $A$ but not of right triangle $B$ the ratio is still $4$, unless length and width describe a rectangle. – Weather Vane Jul 12 '18 at 18:18
• Oh my god, yes I was mistaken. Thank you all for catching my mistake! – geo_freak Jul 15 '18 at 0:28

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.

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

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 $A$

• The question is clear: Areas in Two Similar Right Triangles. – Weather Vane Jul 12 '18 at 18:29
• @WeatherVane reread the last sentence: What is the area of rectangle B in terms of x? – gd1035 Jul 12 '18 at 18:31
• Yes, in which case it's a crap question. – Weather Vane Jul 12 '18 at 18:32