Question

The figure of a wooden frame is given with a picture
inside. If the width of the wood everywhere is
1.2 cm, find the length and width of the picture
and hence the perimeter of the picture.
1.2 cm
1-2
Picture
12,8 cm
1:2
-18.5 cm​

Answer 1

Answer:

Step-by-step explanation:

From the given figure, we can see that the length of the wooden frame is 12.8 cm longer than the length of the picture and the width of the wooden frame is 2 times the width of the picture. Let the length and width of the picture be L and W respectively. Then, we have:

Length of the wooden frame = L + 2(1.2) + L = 2L + 2.4

Width of the wooden frame = W + 2(1.2) + W = 2W + 2.4

Since the width of the wooden frame is twice the width of the picture, we have:

2W + 2.4 = 2L + 2.4 / 2

2W = L - 1.2

We can substitute this expression for 2W into the expression for the width of the wooden frame to get:

2(L - 1.2) + 2.4 = 2W + 2.4

2L - 2.4 + 2.4 = 2W

2L = 2W

L = W

Therefore, the length and width of the picture are equal, and we can solve for them by setting the width of the wooden frame equal to 1.2 cm:

2W + 2.4 = 1.2

2W = -1.2

W = -0.6

This is a negative value, which doesn't make sense in this context. Therefore, we must have made a mistake somewhere in our calculations.

One possible mistake is in the equation 2W + 2.4 = 2L + 2.4 / 2, where we may have misplaced the parentheses. It should be:

2W + 2.4 = (2L + 2.4) / 2

With this correction, we can solve for the length and width of the picture:

2W + 2.4 = (2L + 2.4) / 2

2W = L - 0.6

Substituting L = W, we get:

2W = W - 0.6

W = 0.6

Therefore, the width of the picture is 0.6 cm, and the length of the picture is:

L = W + 1.2 + W = 2.4

The perimeter of the picture is:

2L + 2W = 2(2.4) + 2(0.6) = 5.4 cm