word exercise?

Question

One side of a rectangular stage is 2 meters longer than the other. If the diagnal is 10 meters, then what are the lenghts of the sides?

Answer 1

Let the shorter side me x cm.
(x+2)² + x² = 10² , pythagoras theorem
2x² + 4x + 4 = 100
2x² + 4x -96 = 0
x² + 2x - 48 = 0
(x-6)(x+8)=0
x=6 or x=-8(rejected)
Hence the length of the side is 8cm and 6cm respectively.

Answer 2

Let the smaller side be x, then the bigger side will be x + 2.
So, according to pythagoras theorem =
10^2 = x^2 + (x + 2)^2
So, 100 = x^2 + x^2 + 4 + 4 x
2 x^2 + 4 x - 96 = 0
2 (x^2 + 2 x - 48) = 0
x^2 + 2 x - 48 = 0
x^2 + 8 x - 6 x - 48 = 0
x (x + 8) -6 (x + 8) = 0
(x - 6)(x + 8) = 0
So, x = 6 or x = -8
So, side of a rectangle is always positive. So, x (Smaller side) = 6 cm.
& the bigger side = x + 2 = 8 cm. -:ANS.
Now

Answer 3

The lengths of the sides are A and B. Let A be the longer side. We know that
A = B + 2
and
A^2 + B^2 = C^3
where C is the diagonal (C = 10)

Solving the system of equations (2 equations, 2 unknowns) by substituting one equation into the other, we find that
A = 6 meters
B = 4 meters

Answer 4

Let 1 side of the rectangle be x, so d other side will be (x+2)


By pythagoras theoram

AC² =AB² +BC²
10² =(x+2)² +x²
100=x² +4x+4+x²
0=x² +4x-96+x²
0=2x² +4x-96
0=2x² +2(x-48)
0=(x-6) (x+8)

Thus the possible answer is 6cm and 8 cm

Answer 5

Let X be the short side
Let X+2 be the long side.
The P.T. says X^2 +(X+2)^2 = 10^2 from which it is obvious the sides are 6 and 8. (this is the first integral multiple of the 3/4/5 triangle)

Answer 6

let one side of the rectangle be x

the other is x +2

then by pythagorean theory:

x^2+ (x+2)^2 = 10^2
x^2+x^2 +4x +4 =100

2x^2 +4x - 96 =0

factoring:

(2x+16)(x-6) = 0

only one root makes sense in this problem:

x = 6

the other side is x=8

(note that 6^2 + 8^2 = 100, so we prove the solution is correct)

Answer 7

9.7979m