Answer: length = 8cm; width = 6cm
Step-by-step explanation:
The dimensions of a rectangle are the length and width:
Let x be the length of rectangle, and
y, the width of rectangle
Perimeter equals 2x+2y=28, divide through by 2: x+y=14
Make y the subject, y=14-x, input the value of y into the equation and solve by pythagorean theorem:
x^2 + y^2= 10^2 = 100
x^2 + (14-x)^2 =100
x^2 +196-28x + x^2= 100
2x^2- 28x +196= 100
2x^2 -28x +96 =0
x^2 -14x + 48= 0
(x- 8) (x- 6)= 0
x= 8; or x = 6
The length of rectangle is 8 cm
The width of rectangle is 6 cm
I hope this helps.
