Question

One side of a rectangle is 15 cm longer than three times another side. The area of the rectangle is 150 cm2. Find the length of the shorter side.

Answer 1

Let's call x= length of the shorter side

the long side is 15 + 3 times the shorter side so: 15+3*x

and we know the area of a rectangle is: short side * long side

so

150= x * (15+3*x)

and now we just solve the equation:

$150=15x+3x^2$

To solve this we can use the bhaskara formula

0= 3x2+15x-150

a= 3 b=15 c=-150

bhaskara formula=

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

you replace the values and we get two x:

x1: 5

x2: -10

and length can't be negative so the answer is:

the length of the shorter side is: 5