Respuesta :
Answer:
a) 12.5 cm,
b) 25 cm,
c) 312.5 square cm,
d) For square: [tex]x=18.75[/tex]
For rectangle: [tex]x=12.5[/tex]
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:
[tex]\text{Perimeter of rectangle}=\frac{150}{2}[/tex]
[tex]\text{Perimeter of rectangle}=75[/tex]
We are also told that the length of the rectangle is twice the width of the rectangle, so length of the rectangle would be [tex]2x[/tex].
a) We know that perimeter of the rectangle is twice the sum of its length and width.
[tex]P=2(l+w)[/tex]
Upon substituting our given values, we will get:
[tex]75=2(2x+x)[/tex]
To find width, we need to solve for x.
[tex]75=2(3x)[/tex]
[tex]75=6x[/tex]
[tex]x=\frac{75}{6}[/tex]
[tex]x=12.5[/tex]
Therefore, the width of the rectangle is 12.5 cm.
b) Since length of the rectangle is [tex]2x[/tex], so length of the rectangle would be:
[tex]2x\Rightarrow 2(12.5)=25[/tex]
Therefore, the length of the rectangle is 25 cm.
c) We know that the area of the rectangle is length times width.
[tex]\text{Area of rectangle}=12.5\text{ cm}\times 25\text{ cm}[/tex]
[tex]\text{Area of rectangle}=312.5\text{ cm}^2[/tex]
Therefore, the area of the rectangle would be 312.5 square cm.
d) We already figured out that [tex]x=12.5[/tex] for rectangle.
We know that each side of square is equal, so find x for square, we need to divide 75 by 4 as:
[tex]x=\frac{75}{4}[/tex]
[tex]x=18.75[/tex]
Therefore, the value of x for square would be 18.75 cm.
