• Math

  Dimension Word Problem

  Posted by Varun on June 26, 2023 at 11:27 am

  A rectangular garden has a length that is 4 meters longer than its width. If the diagonal of the garden is 10 meters, what are the dimensions of the garden?

  Hanshika replied 5 months ago 2 Members · 1 Reply
• 1 Reply

• 

  Hanshika

  Member

  December 2, 2023 at 12:47 am

  Helpful

  Up

  0

  Down

  Not Helpful

  ::

  Let the width of rectangle be x

  then length according to question is (x+4)

  Since diagonal of rectangle divides the rectangle into two right angled triangle

  So according to Pythagorean theorem
  

  Diagonal^2= Length^2 + Width^2 ———- (1)

  According to question, Diagonal = 10 m;

  Therefore , putting the values in (1)

  (10)^2=(x+4)^2+x^2

  100 = x^2+8x+16+x^2

  100 = 2x^2+8x+16

  100-16 = 2x^2+8x

  84=2x^2+8x

  dividing both side by 2

  42= x^2+4x

  x^2+4x-42=0

  by the help of quadratic formula

  picture is attached below, from picture value of x=4.73 m

  so x=width= 4.73m

  (x+4) = length= (4.73+4)= 8.73m

  Therefore the dimension of the garden is (8.73*4.73)meters.

  

  • This reply was modified 5 months ago by  Hanshika.

Log In to Reply