Question

Two squares have a total area of 274 square centimetres and the sum of their perimetres is 88 centimetres
Find the side of the larger square.

Answer 1

Answer:

what is the area in cm^2 of the large square ? : Let x = side of the large square then x^2 = it's area : Let y = side of small square

Answer 2

m^2 and total perimeter 52 cm.

what is the area in cm^2 of the large square ?

:

Let x = side of the large square

then

x^2 = it's area

:

Let y = side of small square

then

y^2 = it's area

:

"Two squares have total area 85 cm^2"

x^2 + y^2 = 85

:

" total perimeter 52 cm."

4x + 4y = 52

simplify, divide by 4

x + y = 13

y = (13-x)

:

replace y with (13-x) in the total area equation

x^2 + (13-x)^2 = 85

FOIL

x^2 + 169 - 26x + x^2 = 85

Combine as a quadratic equation

2x^2 - 26x + 169 - 85 = 0

2x^2 - 26x + 84 = 0

Factor this to

(2x-12)(x-7) = 0

Two solutions

x = 7

and

2x = 12

x = 6

:

Area of the larger square: 7^2 = 49 sq/cm

;

:

Check solution

y = 13-7

y = 6 cm

then 6^2 = 36cm is the small square area

total area: 49 + 36 = 85

:

Check the perimeter

49 + 36 = 85;

4(7) + 4(6) = 52