Question

A three and half metre long rod is to be cut into 2 piece,one piece is to be bent into a square and the other into an equilateral triangle.the length of their side must be the same.how should it be cut? solutions

Answer 1

Answer:

The rod should be cut in two parts of length 2 m and 1.5 m.

Given:

• A three and half metre long rod is to be cut into 2 piece,one piece is to be bent into a square and the other into an equilateral triangle. The length of their side must be the same.

To find:

• How should be rod be cut.

Solution:

Let the n be constant.

Concept:

A square and a equilateral triangle are formed by bending parts of rod of 3.5 m, hence addition of their perimeter will be equal to length of rod.

Now, n is constant and side of square = side of triangle.

=> Perimeter of square = 4x...(1)

=> Perimeter of triangle = 3x...(2)

According to the given condition.

from (1) and (2)

=> 4x + 3x = 3.5

=> 7x = 3.5

=> x = 3.5/7

=> x = 0.5 m

Hence,

Length of rod required to make square = 4x

Length of rod required to make square = 4 (0.5)

Length of rod required to make square = 2 m

And remaining for making an equilateral triangle

i.e. 3.5 - 2 = 1.5 m

Hence, the rod should be cut in two parts of length 2 m and 1.5 m.