Question

A rectangular park is to be designed whose breadth is 3m less than its length. It’s are is to be 4m2 more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12m. Find the length and breadth of the rectangular park

Answer 1

Hey

Here is your answer,

Let the breadth of the rectangular path be x and length be (x+3)m.

Area= x(x+3)
=x^2+3x

Area of triangle=1/2 x x x 12
=6x

X^2 +3x = 6x +4
X^2 +3x -6x -4 =0
X^2 +3x - 4 =0
This is the equation

X^2 + 4x -x -4 =0
X(x+4) -4(x+4)=0
X=4
X=-4 (not possible)

The breadth is 4m and length be 4+3=7m

Hope it helps you!

Answer 2

Step1: Equating both the areas.
Step2: Solving the quadratic equation using
$x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a}$
x = b = breadth.
b = -3
a = 1
c = -4
putting these values we get the breadth and on adding three to it we get the length.
Hope this helps... :)