Question

if twice the area of smaller square is subtracted from the area of larger square the result is 14 square cm . if twice the area of larger square is added to three times the area of the smaller square , the result is 203sq cm . determine the side of square

Answer 1

Hi ,

Let side of a smaller square = acm

area of the smaller square (A1 ) = a² ---( 1 )

let side of the larger square = b cm

area of the larger square (A2 ) = b²----( 2 )

according to the problem given,

A2 - 2A1 = 14 sq cm

A2 = 2A1 + 14 ---- ( 3 )

2A2 + 3A1 = 203 sq cm --- ( 4 )

substitute ( 3 ) in ( 4 )

2( 2A1 + 14 ) + 3A1 = 203

4A1 + 28 + 3A1 = 203

7A1 = 203 - 28

7A1 = 175

A1 = 175/7

A1 = 25 sq cm----( 5 )

a² = 5² [ from equation ( 1 ) ]

a = 5 cm

put A1 = 25 in equation ( 3 ) we get

A2 = 2 × 25 + 14

A2 = 50 + 14

A2 = 64

b² = 8² [ from equation ( 2 ) ]

b = 8 cm

Therefore ,

side of the smaller square = a = 5cm

side of the larger square = b = 8cm

I hope this helps you.

:)

Answer 2

Let the ar. of small square be x and larger square be y.
Therefore,
y-2x=14 cm^2 (1)
y=14+2x
Now,
2y+3x=203 cm^2 (2)
On substituting the value of y in equation 2,we get,
2(14+2x)+3x=203
28+4x+3x=203
28+7x=203
7x=203-28
x=175/7
x=25
Therefore,
Ar. of small square= 25 cm^2
Since ar of square= side^2
Therefore,
Side^2=25
Side of small square= (25)^1/2= 5 cm
Ar. of larger square= 14+2x= 14+2×25= 64 cm^2
Therefore the side= (64)^1/2= 8 cm