How do you find the perimeter of a rectangle if you know the diagonal and longer side length?

Question

the diagonal is 13 and the longer side length is 12

Answer 1

Split it into two right triangles and use the pythagorean theorum. a-squared plus b-squared equals c-squared. You have the c of the trianges, that's 13. You have the b, which is 12. Use that formula to find a. Then add 2a+2b to find the perimeter.

Answer 2

It has to do with "a square + b square = c square" The diagonal splits the rectangle into two triangles. So, your equation is: 12 square + b square = 13 square. With me so far? (if not, draw it). then, you have 144 + b square = 169. To get the b square, carry the 144 to the other side, so you have b square = 169-144, which is 25. B is the square root of that, or 5. So, your sides of the rectangle are 12, 12, 5, and 5. Now you can get the perimeter by adding all the sides.

Answer 3

use pythagorean theorem a² + b² = c²

given:
c = diagonal is your hypotenuse = 13
b = width of rectangle = 12

solution:
c² - b² = a²
(13)² - (12)² = a²
169 - 144 = 25

then get the square root of 25 which is = 5

since 5 is your length, 12 is your width
and the formula for perimeter of a rectangle is = 2L +2W

substitute 2(5) + 2(12) = 34units <--- perimeter =)

Answer 4

You know the shorter length is 5 (two sides and diagonal form a 5-12-13 right triangle)

P = 2L + 2W = 2(12) + 2(5) = 24 + 10 = 34

Answer 5

The diagonal forms the hypotenuse of a right triangle with the long side (whose length you know), and the shorter side (whose length you don't know). Therefore:

hypotenuse-squared = longside-squared + shortside-squared

solve for the shortside and you get:
shortside-squared = 13-squared - 12-squared
shortside = 5 (square root of 25)
So the perimeter is 5+12+5+12, or 34

Answer 6

Use the Pythagorean Theorem to compute the third side of the triangle formed by the diagonal and the long side. Then you know both the long and short sides, and can add them together and multiply by two for the perimeter.

Answer 7

If you have the diagnal and the long side, draw a traingle. Use A squared + B squared ='s C squared. A is the short side, B is the long side, and C is the diagnal. A squared + 12 squared (144)='s C squared (169). Therefore A squared must equal 25...which is 5. Short side is 5, long is 12, diagnal is 13.

Area = 60
Perimeter = 34

Answer 8

Pythagorean formula: a ( squared ) + b ( squared ) = c ( squared ) where c is the length of the hypotenuse. You do the math. Once you figure out the length of the shorter side, simply double that and double the longer side for the perimeter.

Answer 9

Use the pythagoras theorem
The shorter side is= sq.rt.[13^2-12^2] = 5
THus perimeter=2*[12+5]=34 units

Answer 10

searching at one quarter of the rectangle, you need to be able to make sure a triangle with radius being the hypotenuse. So 1/2 of the shorter aspect is a million, hypotenuse is 5, for this reason 1/2 of the longer aspect is 2sqrt(6). therefore, the fringe is 8sqrt(6)+4