Question

The base of a triangle is twice as long as a side of a square and their areas are the same. Then the ratio of the altitude of the triangle to the side of the square is:

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $1$
• D. $2$
• E. $4$

Answer 1

The correct option is C $1$

Let h, b be the height and base of the triangle.

Let a be the side of square.

Given b = 2a

Areas are same.

$\frac{1}{2}bh=a^2\frac{1}{2}\left(2a\right)h=a^2\therefore h=a\therefore h:a=1:1⟹\frac{h}{a}=1$

Ratio of the altitude of the triangle to the side of the square = 1