Question

A square and a parallelogram have the same area. If a side of the square is 40m and the height of the parallelogram is 20m, find the length of the corresponding base of the parallelogram.

Answer 1

Answer:

The length is 20 m.

Step-by-step explanation:

Since we have that a square and a parallelogram have the same area and if a side of the square is 40 m and the height of the parallelogram is 20 m, we want to find the length of the corresponding base of the parallelogram.

Then, we know that the area of the square is equal to 40 × 40 = 1600.

Let b be the base of the parallelogram, then the area of the parallelogram is equal to 2(0.5 × 20 × 2b) = 1600 .

Then:

2(10 × 2b) = 1600

⇔ 20 × 4b = 1600

⇔ 4b = 1600/20

⇔ 4b = 80

⇔ b = 80/4

⇔ b = 20 m

Hence, the length is 20 m.

Answer 2

Answer: 80 m

Step-by-step explanation:

Let area of the Square = As

Side of the Square (s) =  40 m

Area of the square is calculated as,

1.  As = (s) x (s) = 40 x 40 = 1600 Sq.m.

Let area of the parallelogram  = Ap

Height of the parallelogram (h) = 20 m

Base length of the parallelogram (b) = ?

Now, area of the parallelogram is given as  

2.  Ap = Height x Base length = (h) x (b)

As we know that areas of square and the rhombus are equal,  

Area of square (As) = Area of the parallelogram (Ap)

Putting the values from the two equations, (1.) & (2.), we get

1600 = (h) x (b)

1600 = 20  x (b)

(b) = 1600 / 20

(b) = 80

Therefore, The length of the corresponding base of the parallelogram is 80 m.