Question

Find the Area and of a rectangle if one of its sides is 12 cm and a diagonal is 37 cm​

Answer 1

Answer:

Area of the rectangle = 420 cm²

Step-by-step explanation:

Given :

One side of the rectangle = 12 cm

Diagonal of the rectangle = 37 cm

To find :

The area of the rectangle

Concept :

To find the area of the rectangle first find the other side of the rectangle.

Use Pythagoras theorem to find the other side of the rectangle

Let ,

AB = 12 cm

AC = 37 cm

AD = Other side

So , the equation will like this -:

$\boxed{\rm{{AD}^{2}+{AB}^{2}={AC}^{2}}}$

After that to find the area of the rectangle use this formula -:

$\boxed{\rm{A=AB\:\times\:AD}}$

Solution :

Other side of the rectangle -:

$:\implies\rm{{AD}^{2}+{12cm}^{2}={37cm}^{2}}$

$:\implies\rm{AD=\sqrt{{37cm}^{2}-{12cm}^{2}}}$

$:\implies\rm{AD=\sqrt{(37\times37)cm-(12\times12)cm}}$

$:\implies\rm{AD=\sqrt{1369-144}cm}$

$:\implies\rm{AD=\sqrt{1225}cm}$

$:\implies\rm{AD=35cm}$

So , the other side of the rectangle is 35 cm

Area of the rectangle -:

$:\implies\rm{A=12cm\times35cm}$

$:\implies\rm{A={420cm}^{2}}$

So , the area of the rectangle is 420 cm² .