![]() If the perimeter and side length of a rectangle are known, subtract the known side length from half of the perimeter to find the other side length. How to Find the Diagonal of a Rectangle Given the Perimeter Since the diagonal is 5 cm and the length is 4 cm, this becomes, which equals. To find the width, knowing the diagonal, use the formula. ![]() įind we need to find the height using Pythagoras’ Theorem. To find the area of the rectangle, use the formula. Example 2:įind the area of a rectangle given that the diagonal is 5cm long and the length is 4cm long. Now we can use to find the diagonal, given that l=10 and w=2. Example 1:įor example, find the diagonal of a rectangle with area 20 m 2 and length of 10 m.įirst divide the area by the length to find the width. Then use the Pythagorean Theorem, d = √(l² + w²), to calculate the diagonal of the rectangle. These two sides are the length (l) and the width (w). If the area and one side of a rectangle are known, divide the area by the known side to find the other side. This can be written as, which equals How to Find the Diagonal of a Rectangle Given the Area If the length and width are both equal to ‘a’, then becomes. The formula for the diagonal length of a square is derived from Pythagoras’ Theorem for the length of the diagonal of a rectangle.įor a rectangle, the diagonal length is given by, where l is the length and w is the width of the rectangle.įor a square, the length and width are equal. Evaluating this, the diagonal length is 14.1cm.įormula for the diagonal length of a square with side lengths ‘a’ For example, the diagonal length of a square 10cm long is d=√2× 10. To find the diagonal length of a square, use the formula d=√2×a, where a is the side length of the square. This becomes and evaluating this, the diagonal is approximately 6.32m long. Substituting these values into the formula, we obtain. The formula for the length of the diagonal of a rectangle Example 1:Ī rectangle has length of 6m and a width of 2m. Evaluating this, d = √40 and therefore the diagonal is approximately 6.32m long. ![]() For example, the diagonal of a rectangle of length 6m and width 2m is given by d = √(6² + 2²). The formula to find the diagonal of a rectangle is d = √(l² + w²), where l is the length and w is the width of the rectangle. Formula to Find the Diagonal of a Rectangle The diagonal is the hypotenuse of the triangle formed by dividing the rectangle in two. Given the length and width of a rectangle, the diagonal is found by squaring these values, adding them and then finding the square root of this. This means that the rectangle is divided into two right-angled triangles from which Pythagoras’ Theorem can be used Total time taken = Total distance walked × time taken to walk 1m.The diagonals of a rectangle are equal in length and divide the rectangle into two congruent triangles. Total distance walked = 5 × Perimeter of the park. If he walks 100m in 5 minutes, how long will it take for him in total? If the size of the park is 100m by 50m, find the distance the boy has walked. Perimeter of rectangle = 2(length + breadth)Įxample 6: Find the perimeter of rectangle whose length is 6 inches and width is 4 inches.Įxample 7: A boy walks 5 times around a park. Perimeter = 2(b) + 2(h) = 2(4) + 2(3) = 8 + 6 = 14.Įxample 5: Calculate the perimeter of the rectangle whose length is 18cm and breadth 7cm Now, substituting these values in the formula for perimeter, we will getĮxample 3: Find the area and the perimeter of a rectangle whose length is 24 m and width is 12m?Įxample 4: Find the area and perimeter of a rectangle whose breadth is 4 cm and the height 3 cm. Therefore, the dimensions are 5cm and 3cm. Note that the value of x must be positive and therefore in our case, the value of x is 2. We can substitute the expressions for length and width into the equation for area in order to determine the value of x. Since the area of a rectangle is given by: We know that the dimensions of the rectangle in terms of x: If its area is 15 cm 2, what are the rectangle's dimensions and what is its perimeter? Thus, the perimeter of the rectangle is 42 cm.Įxample 2: If a rectangle's length is 2x + 1 and its width is 2x – 1. Perimeter of the rectangle = 2(l + w) units The perimeter of a rectangle is the total length of all the four sides.Įxample 1: Rectangle has the length 13 cm and width 8 cm. A rectangle is 2-dimensional however, perimeter is 1-dimensional and is measured in linear units such as feet or meter etc. In rectangle, the distance around the outside of the rectangle is known as perimeter.
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