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