Question

The sum of the areas of two squares is 400 sq.m. If the difference
between their perimeters is 16 m, find the sides of two squares.​

Answer 1

Answer:

s1=16and s2=12

Step-by-step explanation:

s1 square + s2 square is equal to 400

Answer 2

Answer:

12m and 16m

Step-by-step explanation:

Define x and y:

Let the sides of one square be x.

And the side of the other square be y.

The sum of the areas of 2 squares is 400 m²:

x² + y² = 400 ------------ Equation [ 1 ]

The difference in perimeters is 16 m:

4x - 4y = 16

Make x the subject:

4x - 4y = 16

4x = 16 + 4y

x = 4 + y  --------------- Equation [ 2 ]

Substitute [ 2 ] into [ 1 ] to find y:

(4 + y)² + y² = 400

16 + 8y + y² + y² = 400

2y²  + 8y - 384 = 0

2(y + 16)(y - 12) = 0

y = 12 or y = -16 (rejected)

Solve x:

x = 4 + y

x = 4 + 12

x = 16

Find the sides of the two square:

one square = x = 16 m

other square = y = 12 m

Answer: 12m and 16m