Question

The area of a triangle is half the area of a square. If the base of the triangle and a side of the square are equal, what is the ratio of the side of the square to the height of the triangle?

(A) 1 : 1

(B) 1 : 2

(C) 1 : 4

(D) 1 : 6

(E) 1 : 8

Answer 1

The ratio of the side of the square to the height of the triangle is 1 : 2.

Therefore, the correct answer is: option b) 1 :2

Step-by-step explanation:

The ratio of the side of the square to the height of the triangle is 1 : 2.

Let's assume that the base and one of the sides of the square have a length of x.

The area of the square is then x * x = x^2.

Since the area of the triangle is half the area of the square, the area of the triangle is 1/2 * x^2 = (x^2)/2.

The formula for the area of a triangle is 1/2 * base * height. We know that the area of the triangle is (x^2)/2.

Since the base and height of the triangle are equal, we can write:

(x^2)/2 = 1/2 * x * x

(x^2)/2 = (x^2)/2

Hence, the ratio of the side of the square to the height of the triangle is 1 : 2.