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Activity Discussion Math Dimension Word Problem

• # Dimension Word Problem

Posted by 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

Member
December 2, 2023 at 12:47 am
0

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 6 months, 3 weeks ago by  Hanshika.
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