Math, asked by rafiyashaikh0786, 3 months ago

The length of a rectangle is less than twice its breadth by 1 cm. The length of its diagonal is
17 cm. Find its length and breadth.​

Answers

Answered by Anonymous
15

Given :

  • Length of a rectangle is 1 and less than twice its breadth.
  • Length of its diagonal is 17cm.

To Find :

  • Find its length and breadth

Solution :

Let the Length be x

Let the Breadth be y

As given in the question,

x +1 = 2y

x = 2y -1 ---------(1)

we know that diagonal of a rectangle is also divides into two parts and they are right angled triangle

Hence,

By Pythagoras Theorem

 \:  \:   \sf \:   {17}^{2}  =  {x}^{2}  +  {y}^{2}   -  -  -  -  - (2)

Putting x = 2y -1 in equation

 \:  \:  \sf \:  {17}^{2}  =  {(2y - 1)}^{2}  +  {y}^{2}  \\  \\  \:  \:  \sf \:  289 = 4 {y}^{2}  + 1 - 4y -  {y}^{2}  \\  \\  \:  \:  \sf \:  289 = 5 {y}^{2}  - 4y + 1 \\  \\  \:  \:  \sf \: 5 {y}^{2}  - 4y - 288 = 0 \\  \\  \:  \:  \sf \: 5 {y}^{2}  - 40y + 36y - 288 = 0 \\  \\  \:  \:  \sf \: 5y(y - 8) + 6(y - 8) = 0 \\  \\  \:  \:  \sf \: (5y + 36)(y - 8) = 0 \\  \\  \:  \:

we got the values of y as

•y = 8

•y = -36/5

Since length can't be negative hence y = 8cm.

 \:  \:  \sf \: putting \: y = 8 \: in \: equation -  -  -  - (1) \\  \\  \:  \:  \sf \: x = 2(8) - 1 \\  \\  \:  \:  \sf \: x = 15cm

Hence,

  • Length = 15cm
  • Breadth = 8cm

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