the area of a rectangle and square is equal. and the length of the rectangle is 9 more than it breadth . if the area of rectangle is 400 cm² then find the length and breadth of the rectangle and the side of the square
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Answer:
Side of square = 20cm
Length of rectangle = 25cm
Breadth of rectangle = 16cm
Step-by-step explanation:
- * Area of rectangle = 400cm^2 = Area of square
Side of square = √400
= 20cm.
Given that area of square = area of rectangle
lb sq.units = a^2 sq.units.
lb cm^2 = 400cm^2
- Length = 9 + breadth.
(9 + b) (b) = 400
9b + b^2 = 400.
b^2 + 9b - 400
b^2 + 25b - 16b - 400 = 0 {splitting the middle terms}
b (b+25) - 16 (b + 25) = 0
(b - 16) (b + 25) = 0
b = 16 or b = -25.
b = 16 [because the side of a rectangle cannot be negative].
l = 16 + 9 = 25.
Length = 25cm, breadth = 9cm of rectangle and side of square = 20cm
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