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The perimeter of a rectangle is 96 cm. if the ratio of the length to width is 7 : 5, find the dimensions of the rectangle

User Art C
by
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1 Answer

2 votes

Salut/Hello!

Answer: w = 20 cm and l = 28 cm

Explanation:
l - length
w - width
P - perimeter
/ - fraction line
=> - results

we know that P = 2 x (l + w)
we also know that our ratio is l/w = 7/5

l/w = 7/5 => l = 7/5 x w
so now we can go back to the perimeter and replace l

96 = 2 x (7/5 x w + w)
96 = 2 x (7/5 x w/1 + w) Why w/1? - We can't multiply unless w is also in a fraction, so we put it as w/1
96 = 2 x (7w/5 + w)
96 = 2 x (7w/5 + w/1) and we amplify w/1 with 5
96 = 2 x (7w/5 + 5w/5)
96 = 2 x 12w/5
48 = 12w/5
48/1 = 12w/5
48 x 5 = 12w
240 = 12w
w = 20 cm

with that we can find l
96 = 2 x (l + 20)
48 = l + 20
l = 48 - 20
l = 28 cm

I hope it was helpful! :]

User Rosalynn
by
7.2k points