Math, asked by AmanBilal2009, 4 hours ago

The diagonals of a rectangle enclose an angle of measure 78 degrees. If the perimeter of the rectangle is36cm , what is its area?

Answers

Answered by Kalu1303
0

Answer:

The diagonals of a rectangle enclose an angle of measure 78 degree. If the perimeter of the rectangle is 36 cm, what is its area?

Let L & B denote the length & the breadth of the given rectangle respectively.

Hence from above data we get following relations,

L + B = 36/2 = 18

or L = 18 - B

L/B = tan (180° - 78°)/2

or (18 - B)/B = tan 51°

or B = 18/[1 + (tan 51°)] = 8.054 (cm) [Ans]

Step-by-step explanation:

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Answered by Anonymous
1

Answer:

Statement of the given problem,

The diagonals of a rectangle enclose an angle of measure 78 degree. If the perimeter of the rectangle is 36 cm, what is its area?

Let L & B denote the length & the breadth of the given rectangle respectively.

Hence from above data we get following relations,

L + B = 36/2 = 18

or L = 18 - B

L/B = tan (180° - 78°)/2

or (18 - B)/B = tan 51°

or B = 18/[1 + (tan 51°)] = 8.054 (cm) [Ans]

Area = 46.83 cm²

details

The perimeter (P) is 36 cm.

Let L = length and W = width

P = 2L + 2W

L +W = 18 cm

Tan 78° = L/W

L = (Tan 78°)W = 4.705W

4.705W + W = 18

W = 3.155 cm

L = 18 - 3.155 = 14.844 cm

Area = L(W) = (14.844)(3.155) = 46.83 cm²

2a+2b=36 a+b=18

tan((180-78)/2)=a/b a=0.9030861494×b

b=18/1.9030861494=9.4583211621cm

a=8.5416788379cm

8.5416788379 × 9.4583211621=80.7899417124cm² Answer

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