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3 years ago

The perimeter of rectangular room is 144 feet. The length is 3 times the width. Find the area of the room.

Mathematics

1 answer:

zubka84 [21]3 years ago

5 0

Answer:

972 square feet

Step-by-step explanation:

Let x feet be the width of the rectangular room.

The length is 3 times the width, so the length is 3x feet.

The perimeter of the rectangular room is

$P=2(\text{Width}+\text{Length})\\ \\144=2(x+3x)\\ \\144=2\cdot 4x\\ \\144=8x\\ \\x=18\ feet$

Thus,

Width = 18 feet

Length = 54 feet

Find the area of the room:

$A=\text{Width}\cdot \text{Length}\\ \\A=18\cdot 54=972\ ft^2$

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PQ and QR are 2 sides of a regular 12-sided polygon. PR is a diagonal of the polygon. Work out the size of angle PRQ. You must s

dmitriy555 [2]

Answer:

15°

Step-by-step explanation:

A regular polygon is a polygon in which all the sides and angles of the polygon are equal to each other.

A regular 12-sided polygon is a polygon with 12 equal sides and angles.

The sum of interior angles of a polygon is given as:

sum = (2n - 4)90; where n is the number of sides of the polygon

For a 12 sided polygon:

Sum of interior angles = (2 * 12 - 4)90 = (24 - 4)90 = 20 * 90 = 1800°

Therefore since all the angles are equal, each angle = 1800° / 12 = 150°

Therefore in the question, ∠PQR = 150° (angle of a 12 sided polygon), ∠PRQ = ∠QPR = x

Therefore in triangle PQR:

∠PQR + ∠PRQ + ∠QPR = 180°

150 + x + x = 180

150 + 2x = 180

2x = 30

x = 15°

∠PRQ = 15°

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3 years ago