Question

Please help. I'm very confused.???

Answer 1

D.

Explanation:

So, this structure contains metal strips in two distinct places: a) the surrounding, and b) around the colored panes.

Examining the surrounding, it's in the shape of a square, with one side (one metal strip) being `30`cm. Well, the other three sides should be `30`cm as well, so thus far, we know the total length needed is `30+30+30+30=120`cm.

But we still need to identify the total length of metal strips used to separate the panes, IE, the four triangles.

So, since we know the window is surrounded by `30`cm strips on all sides, we know each of these four triangles has a base length of `30`cm.

Now, we're essentially looking for the length of the other two sides.

Let's take an individual triangle, say, the one on the bottom to make things easier to visualize. Draw a perpendicular bisector, a line segment intersecting the base at its midpoint and thereby two `15`cm portions:

Now we have two smaller right triangles, each with a base of `15`cm. Our goal is to find the hypotenuse, the side opposite to the right angle, as each hypotenuse represents a metal strip used to separate the glass panes.

Recall the Pythagorean Theorem, which tells us that `a^2+b^2=c^2`, or, the sum of each leg squared equals the hypotenuse squared.

Well, we still need one more leg length to use the Pythagorean Theorem. We actually have that other leg length! The height of the window overall is `30`cm, so the height of the bisector, which covers half the window, is `15`cm.

`15^2+15^2=c^2`

`c^2=450, c=sqrt(450)`

Simplify `sqrt(450)=sqrt(225*2)=sqrt(225)sqrt(2)=15sqrt(2)`

Now, recall the figure contains `4` of these sides of length `15sqrt(2)` overall. True, we have `4` of the equal triangles in the figure, but do not assume this means we have `8` separate sides -- the triangles share sides.

So, the length of strips coming from these sides is `4(15sqrt(2))=60sqrt(2)`

The total length of strips is thus `120+60sqrt(2)`

D.