the length of the rectangle is 5 cm greater that its breadth. if the length is doubled and breadth tripled then the area of new rectangle increased by the area of original rectangle 70 cm. find the length and breadth of the rectangle.
plz give me solution
Answers
Let the shorter side of triangle =x cm
The other side of the triangle =(x+5)cm
The area of reactangle
(x+5)(x)=150
⇒ x2+5x−150=0
⇒ (x+15)(x−10)=0
⇒ either x=−15 or x=+10
Since the side cannot be negative
Therefore the value of c=−15 is negligible
When x=10cm, then the other side =10+5=15cm
Answer:
Breadth = 2cm
Length = 7cm
Step-by-step explanation:
Let us consider the breadth of the rectangle to be x. Then our length becomes (x + 5)
Breadth = x
Length = x + 5
Area = Length × Breadth
Area of original rectangle = x(x + 5) ⇒ x² + 5x
If the length is doubled and breadth is tripled, we get
New length = 2(x + 5)
New breadth = 3x
New area = 3x(2x + 10) ⇒ 6x² + 30x
New area is 70cm² greater than original area, so we get
6x² + 30x = x² + 5x + 70 ⇒ 6x² - x² + 30x - 5x - 70 = 0
x² + 5x - 14 = 0 ⇒ x² + 7x - 2x - 14 = 0
x(x + 7) - 2(x + 7) = 0 ⇒ (x + 7)(x - 2) = 0
x = -7 or x = 2
As breadth cannot be negative, we get the value of x as 2
We know that length is (x + 5) and breadth is x
Breadth = x ⇒ 2
Length = x + 5 ⇒ 7
Hope this answer helps you.