Sum of areas of two squares is 244 cm and the difference between their perimeter is 8 cm. Find the ratio at their diagonals
Answers
Given:
The ratio of diagonals of squares is 5 : 7.
Formula Used:
Area of triangle = ½ × (Diagonal)2
Calculations:
Let the diagonals of the square be 5x and 7x respectively.
Area of Square1 = ½ × (5x)2
Area of Square2 = ½ × (7x)2
The ratio of their areas = ½ × (5x)2 : ½ × (7x)2
⇒ 25 : 49
Answer:
6:5.
Step-by-step explanation:
Let x be the side of one square and y the side of the other ( smaller) side:
x^2 + y^2 = 244
4x - 4y = 8
x - y = 2
x = y + 2
Substituting for x in y2 + y^2 = 244:
(y + 2)^2 + y^2 = 244
y^2 + 4y + 4 + y^2 = 244
2y^2 + 4y + 4 = 244
y^2 + 2y + 2 = 122
y^2 + 2y - 120 = 0
(y + 12)(y - 10) = 0
y = 10 (length of the side must be positive).
So the length of the other side (x) = 10 + 2 = 12.
The ratio of their diagonals
= ratio of their sides
= 12:10
= 6:5.