Question

. ABCD is a rectangle if AB= 5cm ;
BC = 12cm. Find the diagonal BD

Answer 1

here is the answer using Pythagoras theorem

Answer 2

Given:

AB=5cm

BC=12cm

To find:

The length of the rectangle's diagonal BD

Solution:

The diagonal's required length is 13 cm.

We have a rectangle's diagonal that divides it into 2 equal triangles.

So, BD divides the rectangle into ΔBAD and ΔBCD.

Now, in ΔBAD, AD forms the perpendicular, AB forms the base, and BD is the hypotenuse of the triangle.

The Pythagoras theorem will be used to calculate the required values.

$AD^{2} +AB^{2} =BD^{2}$

Since ABCD is a rectangle, BC=AD=12 cm.

Using the values,

$12^{2} +5^{2} =BD^{2}$

144+25=$BD^{2}$

169=$BD^{2}$

13=BD

Therefore, the diagonal's required length is 13 cm.