![]() Our width is going to beĤ feet, and our length is going to be 6 feet. The length is (4x+1), and the width is x, making it (4x+1) × x. The area of rectangle B is also its length multiplied by its width. The area of rectangle A is its length multiplied by its width, or 3 × x. The areas of the two rectangles add up to 24 obviously. Now, what about 4 and 6? Once again, 4 times 6 is 24. 4x+4x-240 Answer Start by writing this expression shown above. Well, we're gettingĬlose, but it's still not a perimeter of 20. And what's 3 plus 3- isĦ, plus 8 plus 8 is 16. Well, what about- let's see,ģ times 8 is also equal to 24. But what's 2 plus 2? It's 4, plus 12 plus 12. Meet our condition that the perimeter is 20. But what is 1 plusġ plus 24 plus 24? Well, that's going to be Length is longer than the width, that the table is So let's just thinkĪbout the factors of 24. Sure that everything we try out has an area of 24 square feet. Actually, let's do all that- IĬould write it just like that. Times the length- I am going to get to 20. The width- essentially 2 times the width plus 2 Essentially, theįactors of 24, and then figure out which of those So we just have try outĪll of the whole numbers that when I were to take Students graphed their rectangles base (x) vs. Each were given a different base length and had to find height and area. So we really should just beĪble to try out some numbers, because we know that the 'Students were given: Make a rectangle with a perimeter of 40. They tell us that the lengthĪnd width are whole numbers. Learn more algebra, there's fancy algebraic That the width times the length is going to be 24. ![]() And they tell us that theĪrea is 24 square feet. Plus the length plus the length is equal to 20. So these two sides areĪnother way of saying that the width plus the width And this is also, ofĬourse, the width, as well. And then we could call thisĭimension right over here- this is the width. Look something like this- where this dimension The table is longerĪnd width of the table? The length and widthĪre whole numbers. You can also now also factorise to get (x - 2)(x + 3) which might be another question in an exam situation.Rectangular table that has a perimeter of 20 feetĪnd an area of 24 square feet. We disregard the negative number because you cannot have a negative measurement in real life. ![]() Just plug the coefficients into the general formula, together with the value for the discriminant, which you found earlier.įinally, here are the two solutions for x. This is the value of the discriminant part. Therefore, it will have real roots, as opposed to imaginary roots had the number been negative. In this case, it is a positive number 400. This is the bit under the square root sign of the general formula. You always start by calculating the discriminant part. In exam conditions, you may have to solve this equation, in which case you might have to use the general formula for solving quadratic equations. As you can see, we now have a quadratic equation, which is the answer to the first part of the question. We are algebraically subtracting 24 on both sides, so the RHS becomes zero. ![]() In this step, we bring the 24 to the LHS. Since we know the expressions for A and B, we can plug them into the formula A + B = 24 as shown above. You then simply multiply each term in the brackets by x as shown above. Start by writing this expression shown above. If the total area of the building, shaded in yellow, is 24 m² show the following formula. It is a six-sided shape where all the corners are right angles. Here is a floor plan of a building with the following dimensions.
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