Question

a strip of wire of length 32 cm is cut into two pieces. one iece is bent to form a square of side x cm. the other piece is bent to form a rectangle of length lcm and width 3cm. write an expression, in terms of l and x, for the length of the strip wire. show that l=13-2x. the sum of the areas of the squareand the rectangle is represented by S. show that S=x^2-6x+39​

Answer 1

A strip of wire of length 32 cm is cut into two pieces. One piece is bent to form a square of side xcm.

Perimeter of the square = x + x + x + x

= 4xcm

The other piece is bent to form a rectangle of length lcm and width 3cm.

Perimeter of the rectangle = 2(lcm) + 2(3cm)

= 2lcm + 6cm

Write an expression, in terms of l and x, for the length of the strip wire. Show that l = 13 - 2x.

Length of strip wire = perimeter of the square + perimeter of the rectangle

32cm = 4x + (2l + 6)

26 = 4x + 2l

13 = 2x + l

l = 13 - 2x

The sum of the areas of the square and the rectangle is represented by S. Show that S = x² - 6x + 39.

S = Area of the square + area of the rectangle = x² + (l × 3)

= x² + ((13 - 2x) × 3)

= x² + (39 - 6x)

x² - 6x + 39