how to find the length of the diagonal if the length and width of the rectangle are 9 and 12?

Question

3 square root of 2 and 2 square root of 3|

Answer 1

Question 1
d ² = 9 ² + 12 ²
d ² = 81 + 144
d ² = 225
d = 15

Question 2
d ² = (3√2) ² + (2√3) ²
d ² = 18 + 12
d ² = 30
d = √30

Answer 2

By way of explanation...

This problem is trying to disguise a right triangle as two sides of a rectangle and the diagonal. The diagonal, in Pythagorean terms is called the hypotenuse of a right triangle consisting of the length, the width, and the diagonal of a rectangle.

People have referred you to the Pythagorean Theorem, to wit,, The square of the length of the hypotenuse of a right triangle is equal the the sum of the squares of the lengths of the other two sides... written in mathematics...
c² = a² + b²

In your case:
c² = a² + b²
c² = 9² + 12²
c² = 81 + 144
c² = 225
c = 15


People have also referred to 3-4-5 triangles.
There are certain triangles you will run across that integer length sides... or at least sides that are of integer proportions. One of these is a 3-4-5 triangle. This occurs with nauseating frequency... so often in fact that it's helpful to remember it. When with a triangle problem it only takes a quick glance to see if the sides given fit the 3-4-5 profile. In your case 9-12 certainly does.9=3x3, 12=3x4... so the hypotenuse would be 3x5=15. There are actually five such "Pythagorean Triples" with at least one side less than 10. You don't have to sit down and memorize them. But you're going to see a lot of 3-4-5 triangles.

Answer 3

A rectangle will always have 4 90-degree angles. By creating a diagonal, you will see 2 triangles in your rectangle. Both triangles are congruent.

Pick a triangle..makes no difference. Since it will have a right angle, it's a right triangle, and what theorem is infamous when it comes to right triangles? The Pythagorean theorem!

Plug the lengths of your legs (9 and 12) into the formula and you get this:

(9*9) + (12*12) = c[squared]
81 + 144 = c[squared]
225 = c[squared]
c = the square root of 225
c = 15

15 units in length!

Answer 4

The diagonal in this rectangle forms 3,4,5 right triangles so it is 15. If you have to actually calculate it. The √ of the two sides squared and summed is 81+144 = 225. √225 is 15

don't have any idea what you want done with 3√2 and 2√3

Answer 5

simple, a diagonal with length & breadth of a rectangle forms a right angled triangle.
we can apply pythagoras theorem which states: h^2=a^2+b^2 ; where h= lenght of diagonal, a= lenght of rectangle, b=breadth of rectangle
thus h*h=9*9 + 12*12;
h*h=81+144=225;
h=225^0.5;
therefore h=15;

Answer 6

pythagorus - a squared + b squared = c squared

9, 12 => 15

3root2 2 root 3 => root (18 + 12) = square root (30)

Answer 7

The length of the diagonal is
sqrt( 9^2 + 12^2)
= sqrt(81+144)
= sqrt(225)
=15

Remember the 3,4,5 triangle. 9,12,15 is just 3x that one.

Answer 8

= √(9^2 + 12^2)
= √(81 + 144)
= √225
= 15

Answer: 15

Answer 9

15 ... the old A squared + B squared = C squared

Answer 10

it's a 3,4,5 triangle in disguise

The diagonal is 15