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Arisa [49]
4 years ago
12

the width of a rectangle is three more than half the length. its perimeter is 78 centimeters, find the length and width

Mathematics
1 answer:
cupoosta [38]4 years ago
8 0

Answer:

length=l=21

width = w =18

Step-by-step explanation:

 

78 = 2(2w +3 +w)

 

39 = 2w + 3+ w

 

39= 3w + 3

 

36=3w

 

18 =w

 

l=w+3 =18+ 3=21

 

so dimensions are

 

length=l=21

width = w =18

I think this is the answer, if not i'm so sorry :/

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Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle encl
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Answer:

The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units

Step-by-step explanation:

The given parameters in the question are;

The radius of the circle, r = 11

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The measure of angle ∠PAL = 93°

The segment of the circle for which the area is required = Minor segment PL

The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL

The area of a segment of a circle is given by the following formula;

Area of segment = Area of the sector - Area of the triangle

In detail, we have;

Area of segment = Area of the sector of the circle that contains the segment) - (Area of the isosceles triangle in the sector)

Area of a sector = (θ/360)×π·r²

Where;

r = The radius of the circle

θ = The angle of the sector of the circle

Plugging in the the values of <em>r</em> and <em>θ</em>, we get;

The area of the sector enclosed by arc PL and radii AP and AL = (93°/360°) × π × 11² ≈ 98.2 square units

Area of a triangle = (1/2) × Base length × Height

Therefore;

The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units

∴ The area of the segment PL ≈ (98.2 - 60.58) square units = 37.62 square units

Therefore, the area of the shaded segment PL ≈ 37.62 square units

More examples on area of a shaded segment can be found here:

brainly.com/question/22599425

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