Question

Esther cut a square paper vertically to make two rectangle pieces. Each rectangle had a perimeter of 63 inches.

Answer 1

Answer:

Side of the square paper = 21 inches

Step-by-step explanation:

Let the square paper is having measure of each side = a inches

Esther cut this square piece into two pieces.

Let the other side of one rectangle piece = x inches

Perimeter of this piece = 2(a + x) inches

Similarly dimensions of the other rectangular piece will be = a inches × (a - x) inches

Perimeter of this piece = 2[a + (a - x)]

Since both the rectangular pieces have the same perimeter = 63

So, 2(a + x) = 2[a + (a - x)] = 63

2(a + x) = 2(2x - x)

a + x = 2a - x

2a - a = 2x

a = 2x

x = $\frac{a}{2}$

Therefore, Perimeter = 2(a + x) = 2(a + $\frac{a}{2}$) = 63

$2\times \frac{3a}{2}$ = 63

3a = 63

a = 21

Therefore, measure of the sides of the square is 21 inches.