Question

the perimeter of a rectangle is 10 meters and its area is 5 1/4 square centimeter what are the length of its sides? solve this using algebra X and Y​

Answer 1

Answer:

∴ Length of rectangle = x = 7/2 = 3.5 cm

 Breadth of rectangle = y = 3/2 = 1.5 cm

Step-by-step explanation:

Let the length = x

and  breadth = y

Perimeter of rectangle = 2(l + b) = 2(x + y)

2x + 2y = 10

2(x + y) = 10

x + y = 5

y = 5 - x ------ (i)

Area of rectangle = l × b

$5\frac{1}{4} = l . b\\\\\frac{21}{4} = x .y\\\\\frac{21}{4} = x(5 - x)\\\\21 = 4x(5-x)\\\\21=20x-4x^{2} \\\\4x^{2} -20x+21=0\\\\4x^{2} - 14x - 6x + 21 =0 \\\\2x(2x-7)-3(2x-7)=0\\\\(2x-7)(2x-3)=0\\\\2x-7=0\\\\2x=7\\\\x=\frac{7}{2} \\\\x=3.5cm\\\\y=5-x\\\\y=5-\frac{7}{2} \\\\y=\frac{10-7}{2} \\\\y=\frac{3}{2} \\\\y=1.5$

∴ Length of rectangle = 7/2 = 3.5 cm

 Breadth of rectangle = 3/2 = 1.5 cm