Question

find the dimensions of the rectangle whose perimeter is 36 m and which is such that the square of the length of the diagonal is 170m^2

Answer 1

l=11m n b=7m is the answer I think

Answer 2

Answer:

Step-by-step explanation:

Let the sides of the rectangle be of length x

and y

metres. Then the question tells us that the perimeter of the rectangle is 36m

, so

2x+2y=36,(1)

and that the square of the length of the diagonal is 170m2

, and so

x2+y2=170,(2)

by Pythagoras’ theorem.

Rearranging equation (1)

, we find that y=18−x

, and so equation (2)

becomes

x2+(18−x)2=170,

which when we multiply out the brackets becomes

x2+324−36x+x2=170,

and so the quadratic we must solve is

2x2−36x+154=0.

We can divide this equation through by two and solve

x2−18x+77=0.

We can factorise the equation

(x−7)(x−11)=0.

If x=7

, we must have y=11

, and x=11

gives us that y=7

.

Therefore the dimensions of the rectangle are 7m

by 11m

.