Question

the perimeter of a rectangle is 44 cm and the length is given 10 cm then find the diagonal of rectangle​

Answer 1

Step-by-step explanation:

Let,

breadth of rectangle ABCD be 'p'

Given:

ABCD is a rectangle

length of seg AB =10cm

length of seg BC= 'p' cm

Perimeter of rectangle ABCD = 44cm

To find :

length of diagonal AC.

Construction:

Draw a seg AC .

Proof:

length of seg AB =10cm ..... (Given)

breadth of seg BC ='p'cm .......

( Assumption)

Perimeter of rectangle ABCD = 44 cm

..... ( Given)

Perimeter of rectangle= 2(l+b)

44 cm= 2(10 + p)

44 cm = 20+2p

44-20= 2p

22 = 2p

p=22/2

p=11 cm

In ∆ ABC ,

angle ABC=90°

By Pythagoras' theorem,

AC^2= AB^2+BC^2

AC^2 = 10^2+11^2

AC^2= 100+121

AC^2= 221

√AC^2= √221 ...

( Taking square roots on both sides)

AC= √221 cm