Advertisements
Advertisements
Question
The perimeter of a square is numerically equal to its area. Find its area.
Advertisements
Solution
Let each side of the square be x cm.
Its perimeter = 4x,
Area = x2
By the given condition 4x = x2
=> x2 – 4x = 0
=> x (x – 4) = 0
=> x = 4 [x ≠ 0]
Area = x2 = (4)2 = 4 x 4 = 16 sq.units.
APPEARS IN
RELATED QUESTIONS
The perimeter of a square is 36 cm; find its area
The side of a square is 10 cm. If its side is tripled, then by how many times will its perimeter increase?
Your garden is in the shape of a square of side 5 m. Each side is to be fenced with 2 rows of wire. Find how much amount is needed to fence the garden at ₹ 10 per metre
Three squares are joined together as shown in the following figure. Their sides are 4 cm, 10 cm and 3 cm. Find the perimeter of the figure.
In the following figure, each square is of unit length
- What is the perimeter of the rectangle ABCD?
- What is the area of the rectangle ABCD?
- Divide this rectangle into ten parts of equal area by shading squares. (Two parts of equal area are shown here)
- Find the perimeter of each part which you have divided. Are they all equal?
The perimeter of a square garden is 48 m. A small flower bed covers 18 sq m area inside this garden. What is the area of the garden that is not covered by the flower bed? What fractional part of the garden is covered by flower bed? Find the ratio of the area covered by the flower bed and the remaining area.
Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular garden with a length of 60 m and a breadth of 45 m. Who covers less distance?
Avneet buys 9 square paving slabs, each with a side of `1/2` m. He lays them in the form of a square.
- What is the perimeter of his arrangement [Fig (i)]?
- Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [(Fig (ii)]?
- Which has greater perimeter?
- Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)
Two figures can have the same area but different perimeters.
The sum of the lengths of all sides of a square is also called its:
