Question

the longer side of a rectangle is 4cm more than it's shorter side . the area of a rectangle is 320.what are the length of it's sides​

Answer 1

Step-by-step explanation:

length= 4cm

breadth= x

length = 4 + x

area of rectangle= 4+x×x

320= 4+2x

2x=320-4

x=316÷2

x= 158

lenght= 4+x= 4+158= 162

lenght=162cm

Answer 2

Answer:

16 cm and 20 cm

Step-by-step explanation:

As per the provided information in the given question, we have :

• The longer side of a rectangle is 4cm more than it's shorter side.
• Area of rectangle = 320 cm²

We've to find the length of its sides.

Let us suppose its shorter side as x.

↠⠀Shorter Side = x cm… 1)

According to the question, the longer side of a rectangle is 4 cm more than it's shorter side.

↠⠀Longer Side = (4 + x) cm… 2)

As we know that,

★ Area or rectangle = Length × Breadth

↠⠀320 = x( 4 + x )

Performing multiplication using the distributive property.

↠⠀320 = 4x + x² $\;$

Now, transposing 320 from LHS to RHS.

↠⠀0 = 4x + x² – 320

Writing the quadratic equation in the standard form.

↠⠀0 = x² + 4x – 320

By using the middle term splitting method, factorising the expression in RHS.

↠⠀0 = x² + 20x – 16x – 320

Factorising the expression in RHS by taking the common factors.

↠⠀0 = x( x + 20 ) – 16( x + 20 )

Taking (x + 20) as in common in the expression in the RHS.

↠⠀0 = (x – 16)(x + 20)

So,

↠⠀0 = x – 16 Or 0 = x + 20

Or, we can say that :

↠⠀x = 16 or x = – 20

• Negative value will be rejected as the length of the sides can't be negative. Thus,

↠⠀x = 16

⠀⠀_____________________________

❝ Length of the sides : ❞

• Shorter side = x cm = 16 cm
• Longer side = (4 + x) cm = (4 + 16) cm = 20 cm

Therefore, the length of its sides are 16 cm and 20 cm.