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An artist wants to frame a square painting with an area of 400 square inches. She wants to know the length of the wood trim that is needed to go around the painting.

AIf x is the length of one side of the painting, what equation can you set up to find the length of a side?
BSolve the equation you wrote in part a. How many solutions does the equation have?
CDo all the solutions that you found in part b make sense in the context of the problem. Explain.
DWhat is the length of the wood trim needed to go around the painting?

Verified Answer :

Kytten
AA = lw, because it is a square l = w, so 400 = x^2.
Bsquare root both sides. sq rt of 400 = + 20 or - 20. so x = + 20 or - 20.
CNo, -20 does not make sense because distance (length and width) cannot be negative.
DPerimeter is the distance around a shape. Find the perimeter. For a square, P = 4x, so P = 4(20) = 80. So the length of wood needed to go around the painting is 80 inches.

An artist wants to frame a square painting with an area of 400 square inches.

(a) x is the length of one side of the painting

Area of the square formula is  \(A = (side)^2\)

side is x. so area becomes \(A = (x)^2\)

We know Area is 400. so the equation becomes

\(400 = (x)^2\)

(b) Solve the equation \(400 = (x)^2\) for x

\(400 = (x)^2\) (take square root on both sides)

When we take square root we put +-

+-20 = x

x = +20 in  and x=-20in

So there are two solutions for the above equation.

(c)No. we know x is length of the side. the length cannot be negative .

So x=-20 inch is not valid

x=20 inches is our only solution.

(d)To find the length of the wood trim needed to go around the painting, we find the perimeter of the square

Perimeter = 4 side

= 4 x = 4* 20 = 80 inches


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