The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?

Mathematics

1 answer:

Elza [17]3 years ago

7 0

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6 = 20

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1.
$y=mx+b\\\\m=\dfrac{9}{3}=3\\\\b=4\\\\\boxed{f(x)=3x+4}$

2.
$f(x)=-2x+3\\\\for\ x=-2\to f(-2)=-2\cdot(-2)+3=4+3=7\to(-2;\ 7)\\for\ x=-1\to f(-1)=-2\cdot(-1)+3=2+3=5\to(-1;\ 5)\\for\ x=0\to f(0)=-2\cdot0+3=3\to(0;\ 3)\\for\ x=1\to f(1)=-2\cdot1+3=-2+3=1\to(1;\ 1)$

3.
$y=mx+b\\\\m=\dfrac{3}{6}=\dfrac{1}{2}=0.5\\\\b=-3\\\\\boxed{f(x)=0.5x-3}$
$for\ x=-6\to f(-6)=-6\\for\ x=-2\to f(-2)=-4\\for\ x=0\to f(0)=-3\\for\ x=6\to f(6)=0$