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We are given that,

Length of the rectangle is equal to 35 cm, and

Breadth of the rectangle is equal to 12 cm.

First we need to draw a diagonal to the given rectangle.

So, suppose we have a rectangle ABCD and we draw the diagonal AC as,

Now, we are supposed to find the length of AC,

To find it we can use Pythagoras theorem but, first let’s see what does it state,

It states that in a right angled triangle as shown below,

$ {{(hypotenuse)}^{2}}={{(base)}^{2}}+{{(height)}^{2}} $

So we will apply this theorem in $ \Delta ACD $ of the rectangle to find out the value of AC ,

By applying the above theorem in $ \Delta ACD $ we will get,

$ A{{C}^{2}}=A{{D}^{2}}+C{{D}^{2}} $,

$ A{{C}^{2}}={{12}^{2}}+{{35}^{2}} $,

$ A{{C}^{2}}=144+1225 $,

$ A{{C}^{2}}=1369 $,

$ AC=\sqrt{1369} $

$ AC=37 $

Hence we get the length of diagonal of the rectangle as 37 cm.