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Area Calculation MCQ 5: (Lengths of diagonal and width of a rectangle given, to find the perimeter of rectangular area)

A rectangular park measures 8cm on length and it’s diagonals measures 10cm what is the perimeter of the rectangular?

A. 36cm          b) 38cm              c) 28cm            d) 18cm

Solution:

Here we will use Pythagoras theorem for solving this problem.

We have been given following data;

drawit diagram 12

AB= 8 cm

AC= 10 cm

Using Pythagoras theorem for right angled triangle ABC;

\[ (AC)^2= (AB)^2 + (BC)^2 \]

\[ (10)^2= (8)^2 + (BC)^2 \]

\[ 100=64+BC^2 \]

\[ BC^2=36 \]

\[ BC=6 cm \]

Now since opposite sides are equal in a rectangle, so;

AD=BC=6 cm

AB=DC=8 cm

Perimeter is the length of boundary of the rectangle i-e

\[ Perimeter=AB+BC+DA+CD=AB+BC+AD+DC=8+6+8+6=28 cm \]

So the perimeter of the rectangle is 28 cm

 

 

 

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