math rectangle problem?

Hi

Let the width = x, then

Length = x + 1, from the Pythagoras theorem it follows that

(Diagonal of rectangle)^2 = (its length)^2 + (its width)^2

4^2 = (x +1)^2 + x^2 ………….|Diagonal. = 4cms

x^2 + 1 + 2x + x^2 = 16

2x^2 + 2x – 15 = 0

This is a quadratic equation of the form ax^2 + bx + c = 0,

whose Discrimnant D = b^2 – 4ac = 4 -4(2)(-15) = 124

As D is not a perfect square the eqn. cannot be solved

by factorization.

Using formula for quadratic equation,

x = [- b +/- sqrt(D)]/2a

x = [-2 +/- sqrt(124)]/4

x = [-2 +/- sqrt(4*31)]/4 = -(1/2) +/- (1/2)sqrt(31)

as the length of diagonal can not be a negative value

x = -(1/2) + (1/2)sqrt(31)

So width of rectangle = (1/2)[sqrt (31) – 1] = 2.28 cm

Length of rectangle = x + 1 = (1/2)[sqrt (31) + 1] = 3.28cm

Good luck

For the person with the “retarded” comment …. This is a pretty hard little question actually!

The answer above of 1.5 and 2.5 is wrong… sorry. 1.5 + 2.5 equals 4 … that is the sides just stretch the length of the diagonal

Pythagorus theorem sends you around in circles. So trigonometry would be an easier way of solving it.

Take the corner angle and call it a. We’ll call the adjacent Length and the opposite width and W=L-1

We know cos(a) = L/4

sin(a) = (L-1)/4

Then L = 4sin(a)-1

and L=4cos(a)

4cos(a)=4sin(a)-1

4sin(a)-4cos(a)=1

sin(a)-cos(a) = 0.25

I don’t have trig tables with me but find that angle with them and then tan(a) will give you the proportions of the sides to one another.

width = 1.5, length =2.5

use this formula

A squared+ B squared = C squared.

the diagonal is the hypotenuse ( C squared)

width = X

length = X + 1

plug it all in.

using 2 equations 2 unknown technique: 2l + 2w =27 -eq a million l x w =35 -eq 2 using eq2 . l x w = 35 l = 35/w -eq 3 use eq 3 in eq a million 2l + 2w = 27 2( 35/w ) +2w =27 70/w +2w =27 (2w)sqrd + 27w – 70 = 0 Use quadratic equation to remedy for w. once you get w, remedy for l using eq 3

16=(l)squared + (l+i)squared

are you retarded?