Thread: quadratic problem - please get me started

This is the question:
A strand of wire of length 32cm is cut into two pieces. One piece is bent to form a rectangle of width x cm and length (x + 2) cm, and the other piece is bent to form a square.
A) show that the square has sides of length (7 - x) cm.
B) given that the total of the areas enclosed by both the rectangle and the square is 31cm2., form an equation for x and solve t to find the value of x.

I can for example work out that:
x^2 + 2x + 32-(x^2 + 2x)=32

But the x's all cancel each other out so can't work out how to get x?

Can someone give me a helping hand please?

Angus

Originally Posted by angypangy

This is the question:
A strand of wire of length 32cm is cut into two pieces. One piece is bent to form a rectangle of width x cm and length (x + 2) cm, and the other piece is bent to form a square.
A) show that the square has sides of length (7 - x) cm.

rectangle perimeter = 2[x + (x+2)] = 2x + 2(x+2) = 4x + 4

square perimeter = 32 - (4x + 4) = 28 - 4x

square side = (28 - 4x)/4 = 7 - x


B) given that the total of the areas enclosed by both the rectangle and the square is 31cm2., form an equation for x and solve t to find the value of x.

x(x+2) + (7-x)^2 = 31

solve for x

...

Originally Posted by angypangy

This is the question:
A strand of wire of length 32cm is cut into two pieces. One piece is bent to form a rectangle of width x cm and length (x + 2) cm, and the other piece is bent to form a square.
A) show that the square has sides of length (7 - x) cm.
B) given that the total of the areas enclosed by both the rectangle and the square is 31cm2., form an equation for x and solve t to find the value of x.

I can for example work out that:
x^2 + 2x + 32-(x^2 + 2x)=32

But the x's all cancel each other out so can't work out how to get x?

Can someone give me a helping hand please?

Angus

(a) Perimeter of the square = 32-2(x+2)-2x
Length = (28-4x)/4

(b)Area of square = (7-x)^2 and area of rectangle = x(x+2)

(7-x)^2+(x+2)(x)=31

2x^2-12x+18=0

(x-3)^2=0

x=3