The sides of a rectangle are in a ratio. What is the length of the shorter sides of the rectangle if its perimeter is 42 cm?
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To find the length of the shorter sides of the rectangle, we need to know the ratio between the sides. Let's assume the ratio is "x:y".
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the perimeter is given as 42 cm.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Since we have assumed the ratio between the sides as "x:y", let's denote the shorter side as "x" and the longer side as "y".
Thus, we can rewrite the formula for the perimeter as:
42 = 2(x + y)
Simplifying the equation, we get:
42 = 2x + 2y
Divide both sides of the equation by 2:
21 = x + y
Since we are looking for the length of the shorter side (x), we can rewrite the equation as:
x = 21 - y
Now, we need to consider the ratio of the sides. Let's say the ratio between the sides is a:b. This means that x/y = a/b.
Substituting the value of x from the previous equation, we get:
(21 - y)/y = a/b
Now we rearrange the equation to solve for y:
(21 - y)b = ay
Expanding the equation:
21b - by = ay
Rearranging the equation:
21b = ay + by
Factoring out y on the right side:
21b = y(a + b)
Finally, solve for y:
y = (21b) / (a + b)
Now you need to know the actual ratio of the sides (a:b) to find the length of the shorter side (x).
Ratio = 2:5?
P = 42 cm.
X cm = Long side.
2x/5 cm = Short side.
2x + 2*2x/5 = 42 cm.
10x + 4x = 210
14x = 210
X = 15 cm.
2x/5 = 2*15/5 = 6 cm.