Question

A rhombus shaped field has green grass for 18 cows . if each side of the rhombus is 30 m and its longer diagonal is 48m , what is the area of field?
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Answer 1

Answer:

Given:

⇒ABCD is a rhombus

⇒For ΔBCD

Perimeter

=8+30+30

=108 cm

⇒2S=108 cm, S=54 cm

⇒Area of ΔBCD

A=

s(s−a)(s−b)(s−c)

=

54(54−48)(54−30)(54−30)

=

54×6×24×24

=

72×6

=432m

2

⇒Area of field

=2× Area of ΔBCD

=2×432 m

2

=864 m

2

⇒Area of grass field each cow be getting

=

18

864

=48 m

2

solution

Answer 2

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.