In the centre of a rectangular lawn of dimens | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the width of the grass strip around the pond be $x\, m$.Given,the dimensions of the rectangular lawn are $50\, m 	imes 40\, m$.Therefore,the

Vedclass · Accepted Answer

$34, 24$

Vedclass · Answer

(A) Let the width of the grass strip around the pond be $x\, m$.Given,the dimensions of the rectangular lawn are $50\, m 	imes 40\, m$.Therefore,the length of the pond is $(50 - 2x)\, m$ and the breadth of the pond is $(40 - 2x)\, m$.The area of the grass surrounding the pond is given by the difference between the area of the lawn and the area of the pond.Area of grass = (Area of lawn) - (Area of pond)$1184 = (50 	imes 40) - (50 - 2x)(40 - 2x)$$1184 = 2000 - (2000 - 100x - 80x + 4x^{2})$$1184 = 2000 - 2000 + 180x - 4x^{2}$$4x^{2} - 180x + 1184 = 0$Dividing by $4$:$x^{2} - 45x + 296 = 0$$x^{2} - 37x - 8x + 296 = 0$$x(x - 37) - 8(x - 37) = 0$$(x - 37)(x - 8) = 0$So,$x = 37$ or $x = 8$.If $x = 37$,the dimensions of the pond would be negative,which is not possible. Thus,$x = 8$.Length of pond = $50 - 2(8) = 50 - 16 = 34\, m$.Breadth of pond = $40 - 2(8) = 40 - 16 = 24\, m$.Therefore,the length and breadth of the pond are $34\, m$ and $24\, m$ respectively.

In the centre of a rectangular lawn of dimensions $50\, m \times 40\, m$,a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184\, m^{2}$ [see $Fig.$]. Find the length and breadth of the pond. (in $m$)

Similar Questions

The quadratic equation .............. has a root $x=3$.

The product of Virat Kohli's age $8$ years ago and $6$ years later is $680$. Find his present age.

Obtain the roots of the following quadratic equation using the quadratic formula: $\sqrt{3} x^{2} + 10 x - 8 \sqrt{3} = 0$.

Obtain the roots of the following equation using the method of 'completing the square': $5x^{2} - 4x - 10 = 0$.

If the roots of the quadratic equation $3x^{2} + 2\sqrt{5}x - 5 = 0$ exist,find them using the method of completing the square.

Vedclass Test Series

Exam Paper Generator

Online Exam Module