A rectangular balcony is 1 inch wide and 1.75 inches long. If the actual length of the balcony is 7 feet, what is the perimeter

Mathematics

1 answer:

serious [3.7K]3 years ago

6 0

The question is incomplete, complete question is given below.

On the blue print for a house a rectangular balcony is 1 inch wide and 1.75 inches long . if the actual length of the balcony is 7 feet what is the perimeter of the balcony?

Answer:

The perimeter of the balcony is 22 feet.

Step-by-step explanation:

Given,

Actual length = 7 feet

Solution,

In the blue print , length of balcony is 1.75 inches.

The actual length of balcony = 7 feet.

Here we use the unitary method to find out the actual measurement.

$\since\ 1.75\ inches = 7\ feet\\\therefore1\ inch = \frac{7}{1.75} = 4\ feet$

Thus the scale is 1 inch = 4 feet.

On the blue print , the width of the balcony is 1 inch .

So, the actual width = 4 feet

Now,

$Perimeter\ of\ rectangle =2(length+width)$

On substituting the values, we get;

So, the perimeter of the balcony = $2(7+4)$

= $2\times11$

= $22\ feet$

Thus the perimeter of the balcony is 22 feet.

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Solve the given triangles by finding the missing angle and other side lengths.

coldgirl [10]

Answer:

a ≈ 27.65; B = 28°; c ≈ 19.17
a ≈ 163.30; B = 120°; c ≈ 59.77
A = 13°; b ≈ 0.3874; c ≈ 1.3737

Step-by-step explanation:

As long as you're seeking outside help, the use of a suitable tool is appropriate. Many graphing calculators, apps, and web sites are available for solving triangles.

Here, you're given two angles and a side. The third angle is the difference from 180° of the sum of the other two. For example, in the first problem, ...

B = 180° -A -C = 28°

The missing sides are found using the law of sines. Since you are given a side, use that as the reference, and its opposite angle as the reference angle. Then you have ...

side = sin(opposite angle)×<em>((reference side)/sin(reference angle))</em>

Note that the factor in italics remains the same for both remaining sides.

In the first problem, this becomes ...

a = sin(112°)·14/sin(28°) ≈ 27.65

c = sin(40°)·14/sin(28°) ≈ 19.17

The remaining problems are worked in similar fashion.

_____

<em>Comment on triangle solutions</em>

These are straightforward because you're given two angles. If you're given two sides and an angle, the solution method varies depending on which angle you're given (opposite the long side, the short side, or the unknown side). In the last case, the law of cosines is involved. In the second case, there are likely two solutions. Once you have two angles, you can proceed as above.