Q&A for How to Find the Measurement of the Diagonal Inside a Rectangle

Use the Pythagorean Theorem to find the other side. Then multiply the length by the width.

√[(24^2 )+(20^2)] = √576+400 = √976 = 4√61`

Use the Pythagorean Theorem (a^2 + b^2 = c^2). A and B are the lengths of the two sides of the rectangle. To get the length of the hypotenuse, you would need to solve for C. C is the square root of (A squared plus B squared). So c = (a^2 + b^2)^.5.

The length plus the width equals half the perimeter (23). Let x equal the width. So (23 - x) is the length. Therefore, (x)(23 - x) = 120 (the area). Solve for x: (x)(23 - x) = 23x - x² = 120. Then 23x - x² - 120 = 0. Rewrite the equation slightly and multiply both sides by (-1): x² - 23x + 120 = 0. Factor the left side: (x - 8)(x - 15) = 0. x = 8 or 15. That means that the width of the rectangle is either 8 or 15, and the length is the other number. So the width is 8 cm, and the length is 15 cm (because the length is defined as the longer dimension). Use the Pythagorean theorem to find the diagonal: 8² + 15² = the square of the diagonal (d). So 64 + 225 = 289 = d², and d = 17 cm.

Because you cannot find the length and width of a rectangle if all you know is the perimeter and the diagonal, you cannot calculate the area.

Most calculators have a square root button. You can also estimate the value manually if you are familiar with perfect squares. For example, if you wanted to know the square root of 10, you would expect it to be between 3 and 4 since 10 is between 9 and 16 (the squares of 3 and 4, respectively). You would also expect the square root to be closer to 3 than 4, since 10 is much closer to 9 than to 16. (The answer is 3.16.)

Between two hands and two feet, you have four potential contact points. To have three contact points, means you either need to have two feet and one hand or two hands and one foot in contact with the ladder at all times. If you are shifting from two feet and one hand in contact to one foot and two hands in contact (or vice versa), you should always return to the two feet and two hands position first.

If the length and width of a rectangle are 15.1 by 13.0, then you can use the pythagorean theorem to calculate the length of the diagonal since it forms a right triangle. The pythagorean formula is a^2 + b^2 = c^2." Let a=15.1 and b=13. 15.1 squared equals 228.01; 13 squared equals 169; add them together for 397.01. Now we know that c squared must equal 397.01. To solve for c, we take the square root of 397.01, which is 19.925. This answer makes sense because it is longer than both the length and the width.

At least one of the side of the rectangle must be given to easily solve the length. You will just simply square the length given and subtract it to the square of the diagonal. Then, get the square root of the difference. The answer would be the width (or the opposite side) of the rectangle.

If the rectangle is a square, then yes. If the rectangle is not a square, then unfortunately no. If the rectangle is a square, then you can square the diagonal and divide by two to find the area of the square. Then, by square rooting that value, you find the value of the side length.

Remember, to calculate the length of a square using area, we use this equation: Area = Length x Length. Therefore, 2√256 = 4ft = Length of the square.

You cannot find the length and width of a rectangle if all you know is the diagonal, so you can't calculate the area.

A square always has diagonal measurements. A square's diagonal is equal to the square root of twice the square of a side.

There are 192 sixteenths-of-an-inch in a foot (16 x 12 = 192). 2 9/16" is 41/16", and 41 is .21 of 192. 7 7/16" is 119/16", and 119 is .62 of 192. Therefore, 15' 2 9/16" is 15.21 feet, and 44' 7 7/16" is 44.62 feet. Now square those two measurements, and add them together. The square root of that sum will be the diagonal. Thus, (15.21)² + (44.62)² = 231.34 + 1990.94 = 2222.28. √2222.28 = 47.14 feet or about 47' 2/16".

Square the height. Square the length. Square the width. Add those three squares together. Then find the square root of that sum. That's the diagonal.

Let x be one side. The other side will be (34 - x), because half the perimeter is 34. The Pythagorean theorem tells us that 26² = (x)² + (34 - x)². So 676 = (x²) + (1156 - 68x + x²) = 2x² - 68x + 1156). Subtract 676 from both sides: 0 = 2x² - 68x + 480. Divide both sides by 2: 0 = x² - 34x + 240 = (x - 10)(x - 24). So x equals either 10 or 24. Therefore, one side of the rectangle is 10 cm, and the other side is 24 cm.

If it is a square, then you can find the sides using the Pythagorean rule. If it is a rectangle, then you cannot find the diagonals, as the length and breadth can vary.