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La base de un cuadrado sin marco mide el doble de su altura. Si el marco tiene 2 pulgadas de ancho y su área es de 208 pulgadas cuadradas, encuentre las dimensiones del cuadrado sin marco.

Answer :

If the frame has 2 inches of width and its area is 208 inches of square. The dimensions of square without frame is 6.75 and 13.50.

Let the width of rectangle without frame is b.

Let the height of rectangle without frame is h.

Since the base of a square without frame is the double of its height. So

b = 2h...............(1)

The frame has 2 inches of width, so;

The width of rectangle with frame = b + 4

The height of rectangle with frame = h + 4

The area of the rectangle with frame = 208 inches of square

The formula of area of rectangle

A = Height × Width

(h + 4) × (b + 4) = 208

Putting the value of b from the equation 1

(h + 4) × (2h + 4) = 208

Simplify

h(2h + 4) + 4(2h + 4) = 208

2h^2 + 4h + 8h + 16 = 208

2h^2 + 12h + 16 = 208

Subtract 208 on both side, we get

2h^2 + 12h - 192 = 0

Taking common 2 from the equation, we get

h^2 + 6h - 86 = 0

After factoring the equation we get

h = (−3+√95, −3−√95)

h = 6.75, -12.75

The height can't be negative so we use the positive value of h.

Now putting the value of h in the equation 1.

b = 2×6.75

b = 13.50

To learn more about area of rectangle link is here

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The complete question is:

The base of a square without frame is the double of its height, if the frame has 2 inches of width and its area is 208 inches of square. Find the dimensions of the square without frame.

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