Question

A strip of wire of length 150cm is cut into two pieces. One piece is bent to form a square of side x cm, and the other piece is bent to form a rectangle which is twice as long as it is wide. Find expressions, in terms of x, for:
a) the width of the rectangle
b)the length of the rectangle
c) the area of the rectangle
d) calculate the value of x

Answer 1

Answer:

a) 12.5 cm,

b) 25 cm,

c) 312.5 square cm,

d) For square: $x=18.75$

For rectangle: $x=12.5$

Step-by-step explanation:

Let x represent width of the rectangle.

We have been given that a strip of wire of length 150 cm is cut into two pieces. One piece is bent to form a square of side x cm, and the other piece is bent to form a rectangle.

Let us find perimeter of rectangle by dividing the length of the wire by two as:

$\text{Perimeter of rectangle}=\frac{150}{2}$

$\text{Perimeter of rectangle}=75$

We are also told that the length of the rectangle is twice the width of the rectangle, so length of the rectangle would be $2x$.

a) We know that perimeter of the rectangle is twice the sum of its length and width.

$P=2(l+w)$

Upon substituting our given values, we will get:

$75=2(2x+x)$

To find width, we need to solve for x.

$75=2(3x)$

$75=6x$

$x=\frac{75}{6}$

$x=12.5$

Therefore, the width of the rectangle is 12.5 cm.

b) Since length of the rectangle is $2x$, so length of the rectangle would be:

$2x\Rightarrow 2(12.5)=25$

Therefore, the length of the rectangle is 25 cm.

c) We know that the area of the rectangle is length times width.

$\text{Area of rectangle}=12.5\text{ cm}\times 25\text{ cm}$

$\text{Area of rectangle}=312.5\text{ cm}^2$

Therefore, the area of the rectangle would be 312.5 square cm.

d) We already figured out that $x=12.5$ for rectangle.

We know that each side of square is equal, so find x for square, we need to divide 75 by 4 as:

$x=\frac{75}{4}$

$x=18.75$

Therefore, the value of x for square would be 18.75 cm.