PLS HELP (correct gets brainliest, and do all five, if you don't know don't answer!)
pls, show your work!
1. the length of a rectangle is 3 times the width, the perimeter is 96cm, find the width and the length.
2. the length of a rectangle is 5m greater than the width, the perimeter is 150m, find the width and the length.
3. the width of a rectangle is 12cm less than the length, the perimeter is 156cm, find the width and the length.
4. the first side of a triangle is 3m shorter than the second side, the third side is 4 times as long as the first side, the perimeter is 27m, find the length of each side.
5. a triangular sail has a perimeter of 25m, side a is 2m shorter than twice side b, and side c is 3m longer than side b, find the length of each side.
Answers
Answer:
1. Let width be x,
Length of the rectangle = 3x
Perimeter of rectangle = 96cm
Perimeter = 2(Length+Width)
=> 2(3x+x) = 96cm
=> 2(4x) = 96cm
=> 2 * 4x =96cm
=> 4x = 96/2 cm
=> 4x = 48cm
=> x = 48/4 cm
=> x = 12 cm
Length of rectangle = 3x
= 3*12
= 36cm
Width of rectangle = x
= 12cm
Ans. The width of rectangle is 6cm and the hieght is 18cm.
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2. Let the width be x
Length of rectangle = x + 5m
Perimeter of the rectangle = 150m
Perimeter = 2(Length+Width)
=> 2(x+5m+x) = 150m
=> 2(2x+5m) = 150m
=> 2*2x+5m = 150m
=> 2*2x = 150-5 m
=> 2*2x = 145m
=> 2x = 145/2 m
=> 2x = 72.5m
=> x = 72.5/2 m
=> x = 36.25m
Length of rectangle = x + 5m
= 36.25 + 5 m
= 41.25m
Width of rectangle = x
= 36.25m
Ans. The width of rectangle is 36.25m and the hieght is 41.25m.
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3. Let the length be x
Width of rectangle = x-12cm
Perimeter of the rectangle = 156cm
Perimeter = 2(Length+Width)
=> 2(x+x-12cm) = 156cm
=> 2(2x-12cm) = 156cm
=> 2*2x-12cm = 156cm
=> 2*2x = 156+12 cm
=> 2*2x = 168cm
=> 2x = 168/2 cm
=> 2x = 84cm
=> x = 84/2 cm
=> x = 42cm
Length of rectangle = x
= 42cm
Width of rectangle = x - 12cm
= 42 - 12cm
= 30cm
Ans. The width of rectangle is 30cm and the hieght is 42cm.
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4. Let the second side be x
First side of triangle = x - 3m
Third side of triangle = 4(x-3m)
Perimeter of triangle = 27m
Perimeter = First side + Second Side + Third Side
=> x-3 + x + 4(x-3) = 27m
=> x-3 + x + 4*x-3 = 27m
=> 3x -3 + 4*-3 = 27m
=> 3x -3 + (-12) = 27m
=> 3x -3 - 12 = 27m
=> 3x -15 = 27m
=> 3x = 27+15 m
=> 3x = 42m
=> x = 42/3 m
=> x= 14m
First side of triangle = x - 3m
= 14m - 3m
= 11m
Second side of triangle = x
= 14m
Third side of triangle = 4(x-3m)
= 4*11m
= 44m
Ans. The first side of triangle measures 11m, the second side of triangle measures 14m, the third side of triangle measures 44m.
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5. Let the second side be b
First side of triangle = 2b - 2m
Third side of triangle = b + 3m
Perimeter of triangle = 25m
Perimeter = First side + Second Side + Third Side
=> 2b-2m+b+b+3m = 25m
=> 4b-2m+3m = 25m
=> 4b-5m = 25m
=> 4b = 25+5 m
=> 4b = 30m
=> b = 30/4 m
=> b = 7.5m
First side of triangle = 2b - 2m
= 2*7.5m - 2m
= 14m - 2m
= 12m
Second side of triangle = b
= 7.5m
Third side of triangle = b + 3m
= 7.5m + 3m
= 10.5m
Ans. The first side of triangle measures 12m, the second side of triangle measures 7.5m, the third side of triangle measures 10.5m.
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Here you go!