Question

The area of a rectangle is 20 cm^2. The height is 4 cm longer than thrice the width.

Answer 1

Step-by-step explanation:

the lenght is 3x+4

the height is x

the area is

x *3x+4

3x2+4x =20

3x^2 +4x-20=0

by quadratic equations

3x^2 + 10x - 6x -20=0

x( 3x+10) - 2(3x+10)=0

x-2=0

x is 2

OR

3x+10=0

x= -10/3 not possible as side never negative

hence breadth is 2 and length is 10cm

Answer 2

The height is 4 cm longer than thrice the width.

Take the width x.

Then, 4=height-3*width

So, height=3*width+4

Height is 3x+4.

Now we write the quadratic equation x(3x+4)=20

3x²+4x-20=0

By splitting the middle term

3x²-6x+10x-20=0

3x(x-2)+10(x-2)=0

(3x+10)(x-2)=0 ∴x=2 since x>0.

Width : 2 cm, Height : 10 cm