Question

Which is the best equation to use to solve this problem?

The perimeter of a rectangle is 90 ft. The ratio of the length to the width is 8: 7. What are the dimensions of the rectangle?

A. 8x+7x=90


B. 8x+8x+7x+7x=90


C. 8x/7x=90


D. 2x+2x=90

Answer 1

2(a+b)=90

8a=7b

solve the system

Answer 2

i dont understand

Answer 3

UR has demonstrated how this word problem can be reduced to two equations in a and b, with a and b representing the length and width of the rectangle, respectively.

It may be easier for you to grasp what's happening here if you'd draw this rectangle. Label the longer side " a " and the shorter side " b " (noting that you could just as well have used x and y or some other literals).

What does perimeter mean?
What does it mean when we say that the ratio of length to width is 8/7?

Answer 4

Write the formula for perimeter in terms of a and b or x and y, whichever you prefer.

Normally the length of a rectangle is the longer side. We could then literally write an equation showing that the ratio of length to width is 8:7:

\[\frac{ length }{ width }=\frac{ 8 }{ 7 }\].

You need to find a relationship between a and b in the form of a linear equation (Uncle R has already done that for you).

Answer 5

PP: Hope you'll respond in some way.

Answer 6

2(a+8a/7)=90

Answer 7

I am still confused but i am going to guess that it is A.

Answer 8

that cant be right , its not the formula for the perimeter of a rectangle

Answer 9

PP: You're free to do as you wish, but I did suggest steps for you to take. Please refer back to my first two postings.

Answer 10

I'd suggest y ou ask questions, even rudimentary ones, to help yourself get started.

Answer 11

my second guess would be C.

Answer 12

PP: I really want to be of help, but choose not to respond to "guesses." I need to know and understand the reasoning you're using to arrive at answers.

Answer 13

Well i know a ratio is a fraction and because 8:7 is a ratio it is a fraction. 8/7. so that is why i am guessing C

Answer 14

PP: As Uncle R pointed out earlier, we have two "simultaneous equations" and must use both in finding a solution (that is, finding the values of a and b).

have you solved simult eqns before? if so, which method would you apply here?

Answer 15

Here are your "simultaneous equations" (or "system of equations").
Your job is to find either a or b first.

2(a+b)=90

8a=7b

Note that the second can be "solved for a," and that a=(7b)/8 .
Substitute (7b)/8 for a in the other equation. Type out the resulting equation, please.

Answer 16

PP: Please respond so that I'll know you're still involved in finding a solution to this problem.

Answer 17

Sorry my computer is slow

Answer 18

The answer is B