Respuesta :
First we must calculate the diagonal of the rectangle. To do this we must use Pythagoras' Theorem: c^2 = a^2 + b^2, where c^2 is the diagonal and a^2 and b^2 are the length and width of the rectangle.
So we have:
c^2 = 5^2 + 12^2
c^2 = 169
c = 13
The lengths of the two diagonals in a rectangle are equal, therefor the sum of the lengths would be 13*2 = 26
So we have:
c^2 = 5^2 + 12^2
c^2 = 169
c = 13
The lengths of the two diagonals in a rectangle are equal, therefor the sum of the lengths would be 13*2 = 26
The sum of lengths of the two diagonals in a rectangle whose diamentions are 5 by 12 units is 26 units.
What is the diagonal of the rectangle?
The diagonal of a rectangle cuts the rectangle into the two equal right angles. In this the length hypotenuse of the right angle is equal to the measure of the diagonal of the rectangle.
The lenght of the digonal of rectangle is found out using the following formula.
[tex]d=\sqrt{l^2+w^2}[/tex]
Here, (l) is the length of the rectangle and (w) is the width of the rectangle.
The length of the given rectangle is 5 by 12. The length for this rectangle is 12 units and width is 12 units long.
Thus, the diagonal of this rectnagle is,
[tex]d=\sqrt{(12)^2+(5)^2}\\d=\sqrt{144+25}\\d=\sqrt{169}\\d=13[/tex]
The lenght of diagonal of rectangle is 13 units. As both the diagonals of rectangle are equal in measure. Thus, the sum of lengths of the two diagonals in this rectangle is,
[tex]d+d=13+13=26\rm\; units[/tex]
Hence, the sum of lengths of the two diagonals in a rectangle whose diamentions are 5 by 12 units is 26 units.
Learn more about the diagonal of rectangle here;
https://brainly.com/question/17117320
