Question

One side of a rectangle is 12 cm long and its diagonal measure 37 cm. Find the other side and the area of the rectangle.

Answer 1

One side of the rectangle = 12 cm

Diagonal of the rectangle = 37 cm

The diagonal of a rectangle forms the hypotenuse of a right-angled triangle. The other two sides of the triangle are the length and the breadth of the rectangle.

Now, using Pythagoras’ theorem, we have: 

`"(One side)"^2+"(Other side)"^2="(hypotenuse)"^2` 

⇒`(12)^2+"(other side)"^2=(37)^2`  

⇒`144+(Other side)^2=1369` 

⇒`(Other side)^2=1329-144` 

⇒`(Other side)^2=1225` 

⇒`(Other side)=sqrt1225` 

⇒`Other side=35 cm` 

Thus, we have:

Length = 35 cm

Breadth = 12 cm 

Area of the rectangle=`35xx12=420 cm^2`