Question

The length of a rectangle is 5 cm more than its width and the area is 50cm2. find the length, width and the perimeter.

Answer 1

Let Width =x
Then length =5+x
Area=lengthxbreadth=50 cm²
x(5+x)=50
x²+5x-50=0 on solving x=5 or x=-10
x can't be -ve so x=5
Width=x=5cm
Length=5+x=10cm
Perimeter=2(l+w)=2(5+10)=30cm

Answer 2

Given - The length of a rectangle is 5 cm more than its width and the area is 50cm2

To find - Length, width and perimeter

Solution - Let the width of rectangle be x. So, as per the given information, length of rectangle will be = x + 5.

Area of rectangle is calculated by formula length*width.

So, keeping the values in formula to find length and width.

50 = x(x+5)

x² + 5x - 50 = 0

x² + 10x - 5x - 50

x (x + 10) -5 (x + 10)

So, (x - 5) and (x + 10)

Thus, two values of x can be 5 and -10.

Since width can not be negative, so value of x will be 5.

Now, width = 5 cm

Length = x + 5

Length = 10 cm

Perimeter is calculated by the formula = 2(length + width)

Perimeter = 2(5 + 10)

Perimeter = 2*15

Perimeter = 30 cm.

Hence, width is 5 cm, length is 15 cm and perimeter is 30 cm.