Question

Find the sides of a rectangle if the length is 3 less than the width. The perimeter of the rectangle is 54 inches.

Answer 1

Answer:

54 square cm. If the width is 3 less than its length, what is the dimension of the rectangle?

Let the length of a rectangle = l cm

And the width of a rectangle = (l - 3) cm

The area of a rectangle = l×(l - 3) = 54 cm²

Or, l² - 3l = 54

Or, l² - 3l - 54 = 0,

This is a quadratic equation in the standard form ax²+bx+c=0, a, b and c should not be equal to zero.

Where, a=1, b=-3, c=-54

Discriminant = D = b² - 4ac = (-3)² - 4×1×-54 = 9 + 216 = 225 = (15)²

(i) l = (-b+√D)/2a =[-(-3)+√(15)²]/2×1=(3+15)/2=18/2=9

Answer 2

Given :- The length is 3 less than the width. The perimeter of the rectangle is 54 inches.

To Find :- The sides of a rectangle ?

Solution :-

Let us assume that, the width of the rectangle is x inches. .

So,

→ Length of the rectangle = 3 less than the width = (x - 3) inches .

then,

→ Perimeter of rectangle = 2(Length + Width)

→ 2(x - 3 + x) = 54

→ 2x - 3 = 27

→ 2x = 27 + 3

→ 2x = 30

→ x = 15 inches

therefore,

→ Width of the rectangle = x = 15 inches .

→ Length of the rectangle = x - 3 = 15 - 3 = 12 inches .

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