Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
[tex]x=y+5[/tex] ----> equation A
[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)
substitute the equation A in equation B
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]
using a graphing calculator -----> solve the quadratic equation
The solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=y+5 ----> x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]
Answer:
Perimeter of rectangle = 38 cm
Step-by-step explanation:
It is given that, Length of a rectangle is 5 cm longer than the width.
Let 'x' be the width then length = x + 5
Area of of rectangle = x(x + 5)
One side of square = ( x+ 5)/4
Area of all squares = [(x +5)/4]² * 4 = (x + 5)²/4
To find the value of x
Total area = 120 cm²
Area of of rectangle + Area of all squares = 120
x(x + 5) + (x + 5)²/4 = 120
x² + 5x + (x² + 10x + 25)/4 = 120
4x² + 20x + x² + 10x + 25 = 120 * 4
x² + 6x + 5 = 24 * 4
x² + 6x - 96 =0
x = 7
To find the perimeter of rectangle
width = x = 7
Length = x + 5 = 7 + 5 = 12
Perimeter = 2(length + width) = 2(7 + 12) = 38 cm
