Mathematics Answer Note #52

Question 1 a rectangle has a perimeter of 32cm. write down a possible pair of values for its length and width Answer A rectangle is a quadrilateral shape with four sides and four angles, where opposite sides are equal in length and all angles are 90 degrees. The perimeter of a rectangle is the distance around the outside of the shape, which is calculated by adding the lengths of all four sides. Therefore, in order to find a possible pair of values for the length and width of a rectangle with a perimeter of 32cm, we must consider the formula for perimeter, which is: P = 2(l+w) where P is the perimeter, l is the length, and w is the width. Since the perimeter is given as 32cm, we can substitute that into the formula and solve for the values of length and width. This can be done by isolating the variables and solving for either l or w. For this example, let us solve for the length, which would give us the following equation: l = (P/2) - w. Substituting 32 for P, we get l = (32/2) - w, which simplifies to l = 16 - w. Now, we can create a table to find different pairs of values for length and width that satisfy this equation. | Length (cm) | Width (cm) | |-------------|------------| | 15 | 1 | | 14 | 2 | | 13 | 3 | | 12 | 4 | | 11 | 5 | | 10 | 6 | |9|7| |8|8| As we can see from the table, there are multiple pairs of values for length and width that we can choose for a rectangle with a perimeter of 32cm. Some examples include a length of 10cm and a width of 6cm, or a length of 13cm and a width of 3cm. Question 2 calculate the perimeter of an equilateral triangle with sides of 7mm Answer The perimeter of any polygon is defined as the sum of all its side lengths. Therefore, in order to calculate the perimeter of an equilateral triangle with sides of 7mm, we simply need to add up the length of all three sides. In this case, all three sides of the triangle are equal, as it is an equilateral triangle. This means that each side has a length of 7mm. Therefore, the perimeter would be 7mm + 7mm + 7mm, or 21mm. Step-by-step breakdown: 1. Write down the formula for calculating the perimeter of a triangle: P = a + b + c, where P represents perimeter, and a, b, and c represent the lengths of the three sides. 2. Since we are dealing with an equilateral triangle, we know that all three sides are equal. Therefore, we can substitute 7mm for all three variables: P = 7mm + 7mm + 7mm. 3. Use the order of operations to simplify the equation: P = 21mm. Question 3 calculate the perimeter of the rectangle with two sides of 6cm and two sides of 2cm Answer To calculate the perimeter of a rectangle, we need to add all four sides of the rectangle together. In this case, we have two sides with a length of 6cm and two sides with a length of 2cm. Therefore, the perimeter would be 6cm + 6cm + 2cm + 2cm = 16cm. Question 4 calculate the perimeter of a shape with a side of 8cm, two sides of 3cm, one side of 7cm and two sides of 4cm Answer First, let's identify the shape in question. Based on the given dimensions, it appears to be a irregular polygon with five sides. A polygon is a closed shape with straight sides, and the perimeter is the distance around the shape. To calculate the perimeter, we need to add up the lengths of all the sides. The formula for finding the perimeter of a polygon is P = s1 + s2 + s3 + ... + sn, where P is the perimeter and s1 through sn are the lengths of the sides. Using the given dimensions, we can plug them into the formula: P = 8cm + 3cm + 3cm + 7cm + 4cm + 4cm = 29cm. Therefore, the perimeter of the shape with sides of 8cm, two sides of 3cm, one side of 7cm, and two sides of 4cm is 29cm. Question 5 calculate the perimeter of a triangle with two sides of 9cm and one side of 4cm Answer To calculate the perimeter of a triangle with two sides of 9cm and one side of 4cm, we will use the formula: perimeter = side1 + side2 + side3. Step 1: Identify the given sides In this case, we are given two sides of 9cm and one side of 4cm. Let's label these sides as side1 = 9cm, side2 = 9cm, and side3 =4cm. Step 2: Substitute values into the formula Using the formula, we can calculate the perimeter by adding the three sides together: perimeter = side1 + side2 + side3 perimeter = 9cm + 9cm + 4cm Step 3: Simplify the expression To simplify, we can add the like terms together: perimeter = 18cm + 4cm perimeter = 22cm So, the perimeter of the triangle with two sides of 9cm and one side of 4cm is 22cm.