The length of a rectangle is 5cm more than its width and the area is 50cm². Find the length, width and the perimeter
Answers
length of rectangle=5 + x
width of rectangle =x
area of rectangle=50 cm2
ATQ
x(5+x)=50
5x+x2=50
x2+5x-50=0
x2+10x-5x-50=0
x(x+10)-5(x-10)=0
(x-5)(x+10)=0
x-5=0
x =5
x+10=0
x=-10
width =5 length =5+5=10
Given:
The length of a rectangle is 5cm more than its width
The area of the rectangle=50cm2
To find:
The length, width, and perimeter of the rectangle
Solution:
The length, width, and perimeter of the rectangle are 10cm, 5cm, and 30cm, respectively.
We can find the measurements by following the steps given below-
Let the width of the rectangle be W.
The length is 5 cm more than the width.
So, the length of the rectangle=W+5
The area of a rectangle= Product of its length and width
Area=(W+5)W
50=W(W+5)
50= W²+5W
W²+5W-50=0
Now we will solve the quadratic equation to find the measurements.
Solving the equation to find the value of W,
W²+10W-5W-50=0
W(W+10)-5(W+10)=0
(W-5)(W+10)=0
Putting W-5 and W+10 equal to 0, we get
W=5, -10
We got two values of which one is negative.
Since the width of a rectangle can't be negative, Width, W=5cm.
So, the length=W+5=5+5=10cm
We have the dimensions to calculate the perimeter of the rectangle.
The perimeter of a rectangle =2(length+width)
Perimeter=2(10+5)
=2×15
=30cm
The length, width, and perimeter of the rectangle are 10cm, 5cm, and 30cm, respectively.