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3 years ago

The length of a rectangle is 2 km less than 3 times the width. If the perimeter is 68 km,What is the length of the rectangle

Mathematics

1 answer:

11111nata11111 [884]3 years ago

6 0

Answer:

The length of the rectangle is 25 km

Step-by-step explanation:

Let

x ----> the length of rectangle

y ----> the width of rectangle

we know that

The perimeter of rectangle is

$P=2(x+y)$

we have

$P=68\ km$

$68=2(x+y)$

simplify

$34=(x+y)$ ---- > equation A

$x=3y-2$ ---> equation B

substitute equation B in equation A and solve for y

$34=(3y-2)+y$

$34=4y-2$

$4y=34+2$

$4y=36$

$y=9\ km$

Find the value of x

$x=3(9)-2=25\ km$

therefore

The length of the rectangle is 25 km

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Step-by-step explanation:

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$A=(0,0)\\B=(1,1)\\C=(4,-2)\\D=(3,-3)$

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$Slope\,\,for\,\,AB=\frac{1-0}{1-0} =1\\\\Slope\,\,for\,\,CD=\frac{-3+2}{3-4} =1\\\\Slope\,\,for\,\,AD=\frac{-3-0}{3-0} =-1\\\\Slope\,\,for\,\,BC=\frac{-2-1}{4-1} =-1\\\\So,AB||CD\,\,and\,\,AD||BC$

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