Question

wire A is bent to form an equilateral triangle and the wire B is bent in the form of a square such that the area covered by the triangle and the square is the same .what is the ratio of the length of wire A to wire B​

Answer 1

sorry the answer was wrong

Answer 2

Given:

Wire A is bent to form an equilateral triangle.

Wire B is bent to form a square.

The area of both the square and the triangle is the same.

To find:

The ratio of the length of wire A to B.

Solution:

Let,

Length of the side of the triangle be a.

The total length of wire A = 3a

Length of the side of the square be x.

The total length of wire B = 4x

Now, given that

Area of square = Area of triangle

$x^2$ = $\frac{\sqrt{3} }{4} a^2$

$a^2$ = $\frac{4}{\sqrt[n]{3} } x^2$

a = 1.519 x

Now,

Ratio = $\frac{3a}{4x}$

= $\frac{3(1.5x)}{4x}$

=$\frac{4.5}{4}$

=$\frac{9}{8}$

Therefore, the ratio of lengths of wire A to wire B will be 9/8.