Question

The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are its dimensions?
Could someone explain to me how I would start this? Please :) <3

Answer 1

Step one, read the problem carefully. Make sure you understand what the words mean. Look the words up in a dictionary or online if you don't understand certain words.

Step two, draw a picture of the problem if possible.
Step three, see if the units are same. If different, then you will probably need to make a conversion.

Step four assign variables from parts of the problem that are unknown.
Step five write an equation.
Step six solve the equation.
Step seven check your answer. Does it make sense.

Answer 2

Step one, read the problem. Two terms in the problem that you need to know are: rectangle and parameter.

What do you know about rectangles. We should know that opposite sides of a rectangle are equal in length.

What do you know about parameter of a rectangle? We should know that for the parameter of a rectangle we add the lengths of all four sides.

Step two, draw a picture of a rectangle. Label the two shorter sides width. Label the two longer sides length.

Step three, check the units. Are they the same? We see that the length is in centimeters (cm) and the parameter is in centimeters (cm). So the units are the same, and we don't need to make any conversions.

Answer 3

Step four, assign variables to unknown parts of the problem. In this problem we don't know the width. So assign the variable w for width. We are given that the length is 4 times the width plus an additional 9.7 centimeters (cm). So the length is 4w + 9.7

Answer 4

Step five, write an equation. Since we need to add all four sides of a rectangle to find the parameter, and opposites sides of a rectangle are equal in length, our equation should look like this.

w+w+4w+9.7+4w+9.7=91.4

Simplify by adding like terms.

10w +19.4 = 91.4

Rearrange the equation to get the variable on one side of the equation by subtraction 19.4 from both sides.

10w = 91.4-19.4
10w = 72

Divide both sides by 10

w=7.2 centimeters (cm)

Answer 5

Step seven, check your answer. Does it make sense?

So add all four sides.

7.2+7.2+ 4(7.2)+9.7 + 4(7.2) +9.7 = perimeter

Simplify

7.2 + 7.2 + 28.8 + 9.7 + 28.8 + 9.7 = perimeter

91.4 = perimeter.

So the answer checks.

Answer 6

Ah, thank you, this makes a lot more sense :)

Answer 7

yw