Question

19. A piece of wire 44 cm long is cut into two parts.

Each part is bent to form a square. Given that
the total area of the two squares is 65 cm², find the
perimeter of each square.

Answer 1

Answer:28 and 16 cams

Step-by-step explanation: let the two parts be x cms and 44 -x cms.

So side of squares will be x/4 and (44-x)/4 resp

Area will be (x/4)^2 and ((44-x)/4)^2 resp

Equation is(x/4)^2 + ((44-x)/4)^2 = 65

(X-28)(x-16) = 0

X =28 or x = 16 cms

Answer 2

A = x^2 + y^2 = 65 cm^2

4x + 4y = 44 cm

This is a system of equations where you can solve for one variable and then substitute to find the other.

4x = 44 - 4y

X= 11-y

Then, substitute.

(11-y)^2 + y^2 = 65

121-22y+2y^2=65

2y^2-22y+56= 0

Now factor and solve for y.

Y^2-11y+28=0

(Y-4) (y-7) =0

Y= 4 or 7

The perimeter is 4(x) + 4(y), so the perimeters of the squares would be 28 cm and 16 cm respectively.