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Drupady [299]
2 years ago
15

the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 56 in, find its length and width

Mathematics
1 answer:
lisabon 2012 [21]2 years ago
3 0

Answer:

Step-by-step explanation:

Let the width of the rectangle = x

As length is 5 inches longer than width, we have to add 5 to width

Length = x + 5

Perimeter of ractangle = 56 in

2* (length + width) = 56

2*( x + 5 + x) = 56

2* (2x + 5)    = 56

Use distributive property: a*(b +c) =(a*b) + (a * c)

2*2x + 2*5   = 56

4x  + 10 = 56

Subtract 10 from both sides

4x = 56- 10

4x = 46

Divide both sides by 4

x = 46/4

x = 11.5

Width = 11.5 in

length = 11.5 + 5

            = 16.5 in

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Answer:

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Step-by-step explanation:

77. Left hand side

= \cot^{6} x

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{Since we know, \csc^{2} x - \cot^{2}x = 1}

= \cot^{4} x \csc^{2}x - \cot^{4} x  

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78. Left hand side

= \sec^{4}x \tan^{2} x

= \sec^{2} x [1 + \tan^{2}x] \tan^{2} x  

{Since \sec^{2}x - \tan^{2}x = 1}

= \sec^{2}x [\tan^{2}x + \tan^{4}x ]

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79. Left hand side  

= \cos^{3} x\sin^{2} x

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{Since \sin^{2}x + \cos^{2} x = 1}

= [\sin^{2}x - \sin^{4}x] \cos x

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80. Left hand side  

= \sin^{4}x - \cos^{4}x

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{Since \sin^{2}x + \cos^{2} x = 1}

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Answer:

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Step-by-step explanation:

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