Expression for area of a rectangle12/19/2023 We disregard the negative solution, as you cannot measure a negative amount in real life. Therefore, 3 cm is the length of the smaller rectangle. In the third step, you plug the rest of the coefficients including the discriminant into the formula to find the solutions for x.įinally, these are the solutions. As you can see, it is a positive number, which means that the roots will be real. In the second step, you calculate the discriminant, which is the bit under the square root sign of the standard formula. Next Area of a Semi-Circle Practice Questions. Previous Area of a Parallelogram Practice Questions. The first step is to identify the coefficients a, b, and c as shown above. Area of a Rectangle Practice Questions Click here for Questions. To find the length of the smaller rectangle, you simply have to solve the quadratic equation, using the standard formula. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. The area of a rectangle depends on its sides. As you can see, we have a quadratic equation, which is the answer to the first part of the question. Definition: Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The formula for the area of a rectangle and the. Subtract both sides by 21 to bring it over to the LHS. area of a rectangle and the area of a triangle alike and different Explain. We simply plug the expressions of the individual areas of A and B into the expression A - B = 21. The area of the small rectangle B is 2 × x, which is the multiplication of the length of its sides. The area of the large rectangle A is (2x+3) × x, which is the multiplication of the length of its sides. If you subtract the area of the small rectangle from the area of the large one the resulting area shaded in yellow equates to 21. We reject the answer x 5 9 because BC 2x 2( 5 9) 10 9 would have negative length. For instance the perimeter of the rectangle of Example 6.1.1 would be 5 + 5 + 3 + 3 16. The perimeter of a polygon is the su.m of the lengths of its sides. If the area of the large rectangle is A, and the area of the small rectangle is B, then we can write the expression above. The area of a square is the square of one of its sides. AnswerĬutout area problems are very simple to solve. Show that 2x²+x-21=0, and calculate the length of the smaller rectangle. The small rectangle has a length x and width 2 cm. A small rectangle is missing from one corner. The diagram above shows a large rectangular piece of card of length 2x+3 and width x. I have designed the question so that the numbers can be easily calculated without a calculator. The final expression is of course a quadratic equation that you can solve using the standard formula. In this example question, there are two rectangles, and you simply have to subtract the area of the smaller rectangle from the area of the larger rectangle to get the answer.
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