The perimeter of a rectangle is 28 cm. The length is 10 cm longer than the width. What are the length and width of the rectangle
Answers
The length= x
The width= y
Perimeter is 28 cm, so...
Equation 1
x+x+y+y=28
2x+2y=28
x+y=14
x=14-y
Length is 10 com longer than width, so...
Equation 2
x-y=10
Substitute Equation 1 into Equation 2
x-y=10
14-y-y=10
-2y=-4
y=2
Substitute y=2 into Equation 1
x=14-y
=14-2
=12
Answer: Length=12 cm, Width=2 cm
Final answer:
The length of the rectangle is 12 cm and the width is 2 cm.
Explanation:
To solve this problem, you have to understand that the perimeter of a rectangle is given by the formula 2(length + width). You are given that the perimeter is 28 cm, and the length is 10 cm longer than the width. Let's denote the width as 'w'. So, the length would be 'w + 10 cm'. Substituting into the formula, we have:
2((w + 10) + w) = 28
which simplifies to:
2(2w + 10) = 28
4w + 20 = 28
Subtract 20 from each side:
4w = 8
Finally, divide each side by 4 to solve for 'w':
w = 2 cm. The width is 2 cm and the length, which is 10 cm more than the width is 12 cm.
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Please give me brainiest!
Answers
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Answers
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