Question

if the perimeter of a rectangle is 68cm. if the diagonal is 6cm find the dimentions of the rectangle. solved using simultanious equations
?

Answer 1

perimeter of a rectangle is given by, 2L +2B= 68
, where L is length and B is breadth.

diagonal can be formed by using Pythagoras theorem,
6^2 = L^2 + B^2
36 = L^2 + B^2

From 2L +2B= 68,
Rearrange to form, L = (68-2B)/2 = 34 -B
Substitute L = 34-B to the diagonal equation

36 = (34 -B)^2 + B^2
36 = 1156- 68B + B^2 + B^2
2B^2 - 68B + 1120 = 0
B^2 - 34B + 560 =0

And here im stuck, because there is no solution for B

I believe there is an error in the question.

Pretty sure the diagonal cannot be just 6cm

Answer 2

sorrry the diagonal is 26 mmy keyboard didnt work properly, sorry for inconvenience

Answer 3

Damn.
Continuing from the substitution.
26^2 = (34 -B)^2 + B^2
676 = 1156- 68B + B^2 + B^2
2B^2 - 68B + 480 = 0
B^2 - 34B + 240 = 0

Solving quadratic equation,
(B-10)(B-24) = 0

B = 10 or B= 24

Remember that 2L +2B= 68
L +B = 34

When B = 10
L +10 = 34
L = 24

When B = 24
L + 24 = 34
L = 10 This is rejected because length must be longer than breadth.

Thus length of rectangle is 24 while breadth is 10.

Answer 4

thanks

Answer 5

Np. hope you understand the workings.

Answer 6

yeah thanks theyre nice and clear