Question

if 4 times the area of a smaller square is subtracted from the area of a larger square,the result is 144m^2 The sum of the areas of the two squares is 464 m^2 Determine the sides of the two squares.

Answer 1

$\textbf{Answer}$

$\textbf{Lets suppose that,}$
Area of smaller square is x m^2
&
Area of larger square = y m^2

According to the question,
$\textbf{y - 4x = 144 -----------(1)}$

Since sum of areas of both square is 464 m^2
=> $\textbf{x + y = 464 -------(2)}$
=> $\textbf{x = 464 - y --------(3)}$

Putting value of x in equation (1),
y - 4x = 144
=> y - 4(464 - y) = 144
=> y - 1856 + 4y = 144
=> 5y = 144 + 1856
=> 5y = 2000
=> y = 400

Putting value of y in equation (3),
x = 464 - y
=> x = 464 - 400
=> x = 64

Smaller square's area = 64 m^2
=> Smaller square's area = 8^2 m^2
We know that area of a square = (side)^2
=> $\textbf{Side of smaller square = 8 m}$
Larger square's area = 400 m^2
=> Larger square's area = (20)^2 m^2
As area of a square = (side)^2
=> $\textbf{ Side of larger square = 20 m}$



$\textbf{Hope It Helps}$

$\textbf{Thanks}$

Answer 2

Let side of smaller square is (√b) m
And side of larger square is (√a) m


Hence, Area of smaller square is ( b ) m^2 and Area of larger square is ( a ) m^2




Given, 4 times the area of smaller square - area of larger square = 144 m^2

a - 4 ( b ) = 144 m^2

a - 4b = 144

a = 144 + 4b ----1equation



Sum of areas of squares = 464 m^2

a + b = 464



Putting the value of a from 1equation,


=> 4b + 144 + b = 464

=> 5b = 464 - 144

=> 5b = 320

$=> b = \frac{320}{5}$

=> b = 64




Putting the value of ( b ) in 2equation,

=> a + b = 464
=> a + 64 = 464
=> a = 464 - 64
=> a = 200



Hence,

Area of smaller square is b = 64 m^2

Therefore, side of smaller square is (√64 m^2) => 8 m



Area of larger square is a = 400 m^2

Therefore, side of larger square is (√400 m^2) => 20 m