Writing equations to represent geometric problems
About this video
A rectangle has sides 4x + 2 and 2 1/2, a perimeter of 17x units and an area of 15x square units. Sal writes a perimeter equation by adding all four sides and setting the sum equal to 17x, and an area equation by multiplying 2 1/2 by (4x + 2) and setting it equal to 15x, without solving either.
You'll be able to
- write an equation for the perimeter of a rectangle with algebraic side lengths.
- write an equation for the area of a rectangle with algebraic side lengths.
- recognise different equivalent ways to write the same equation.
Key words
- perimeter
- The total length around a shape, found by adding all its sides.
- area
- The amount of space inside a shape; for a rectangle, base times height.
- equation
- A statement that two expressions are equal, using an equals sign.
Transcript
- [Instructor] We're told the perimeter of the rectangle shown is 17x units. The area of the rectangle is 15x square units. Write an equation that represents the perimeter, and also write an equation that represents the area. So pause this video and see if you can write those two equations.
All right, now let's do this together. So let's tackle this first one. Write an equation that represents the perimeter. So, the perimeter is going to be the length of all of the sides. So you have this side right over here, which is 4x + 2, and then you're going to add this side over here, which is...
So it's gonna be plus 2 1/2, plus this side over here, which is going to be 4x + 2 again. So plus 4x + 2, plus this side, which is going be 2 1/2, plus 2 1/2. Well, that's going to be equal to the perimeter, which they told us is 17x units. So that is going to be equal to 17x, and we're done.
That's all they wanted. They just want us to write an equation that represents the perimeter. We don't have to solve it. So now let's do the same thing for the area. The area of a rectangle is going to be our base times our height, or our height times our base.
So we could say it's 2 1/2 times 4x + 2, 4x + 2, and then that's going to be our area, which they say is 15x square units. So that's equal to 15x. We could have also written it the other way. We could have said that the area which is 15x is equal to 2 1/2, the height, times 4x + 2.
So a lot of different ways to approach it. But in both cases, we are now done.
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