The area of a rectangle is 84cm2. If the length is 5cm longer than the width,find the length of the rectangle.
Answers
Given,
- The area of a rectangle is 84 cm².
- The length is 5 cm longer than the width.
To find,
The length of the rectangle.
Solution,
Let the width be x cm.
So, length = (x+5) cm.
Area = 84 cm²
According to condition,
x × (x+5) = 84
or, x²+5x = 84
or, x²+5x-84 = 0
Consider the form x²+bx+c. Find a pair of integers whose product is c and sum is b. In this case we have to find a pair of integers whose product is 84 and sum is 5.
The integers are (-7) and 12.
∴ (x-7)(x+12) = 0
Therefore, (x-7) = 0
or, x = 7.
And, (x+12) = 0
or, x = -12.
∴ x = 7 and (-12).
Since the width of a rectangle can't be negative, we will take x as 7.
So,
Breadth = x cm = 7 cm.
Length = (x+5) cm = (7+5) cm = 12 cm.
Hence,
The length of the rectangle is 12 cm.
Verify,
( length × breadth) = area
( 7 × 12 ) cm² = 84 cm²
or, 84 cm² = 84 cm²
∴ L.H.S = R.H.S.