Question

a piece of wire 120 cm in length is to be cut into two pieces, one to form rectangle and the other an equilateral triangle. The length of the rectangle is to be three less than twice of the width, and each side of the triangle is to be twice the length of rectangle. find the length of each piece of wire.

Answer 1

Let the width of the rectangle be xcm
Then the length of the rectangle = 2x - 3
Then the length of the triangle = 2(2x - 3) = 4x - 6
Perimeter of the rectangle = 2(l+w)
⇒2(2x - 3 + x)
⇒2(3x - 3)
⇒6x - 6
Perimeter of the equilateral triangle = 3a
⇒3(4x - 6)
⇒12x - 18
The perimeter of the rectangle + perimeter of the triangle = 120cm
⇒6x - 6 + 12x - 18 =120
⇒18x - 24 = 120
⇒18x = 120 + 24
⇒18x = 144
⇒x = 144/18
∴x = 8cm
One part = perimeter of the rectangle
⇒6x - 6
⇒6* 8 - 6
⇒48 - 6
⇒42cm
Another part = perimeter of the triangle
⇒12x - 18
⇒12* 8 - 18
⇒96 - 18
⇒78cm
∴The two parts are of the length 42cm and 78cm.