If the width of rectangle ABCD is 8 cm and the length of diagonal line AC is 14, find the length of rectangle ABCD. A2 + b2 = c2. 64+ b2 =196. square root of b2 = square root of 132. B =2square of 33. L = ?

L=B

To find the length of rectangle ABCD, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we can consider rectangle ABCD as a right triangle, with the width as one side (let's call it a) and the length as the other side (let's call it b). The diagonal line AC acts as the hypotenuse (let's call it c).

We know that the width (a) is given as 8 cm, and the diagonal line AC (c) is given as 14 cm.

So, using the Pythagorean theorem, we have:

a^2 + b^2 = c^2

Substituting the known values, we have:

8^2 + b^2 = 14^2

Simplifying this equation, we get:

64 + b^2 = 196

To isolate b^2 on one side of the equation, we can subtract 64 from both sides:

b^2 = 196 - 64

b^2 = 132

To find the value of b, we can take the square root of both sides:

√(b^2) = √132

b = √132

Now, to evaluate the value of √132, it comes out to be approximately 11.4891.

Therefore, the length of rectangle ABCD (b) is approximately 11.4891 cm.