Math Problem Need help? Thank You?

Question

I know that this problem may be simple but I can't get the right answer for it. Can You help me please. Is there a solution to this question. The question is( Find the dimensions of a rectangle if the diagonal is 2 more than the longer side, which in turn is 2 more than the shorter side.) Thank You very much.

Answer 1

let

x = short let

x + 2 = long leg

x + 4 = diagonol

- - - - - - --

Pythagorean Theorem

c² = a² + b²

(x + 4)² = (x + 2)² + x²

x² + 8x + 16 = x² + 4x + 4 + x²

x² + 8x + 16 = 2x² + 4X + 4

x² + 8x + 16 - x² = 2x² + 4x + 4 - x²

8x + 16 = x² + 4x + 4

8x + 16 - 8x = x² + 4x + 4 - 8x

16 = x² - 4x + 4

16 - 16 = x² - 4x + 4 - 16

0 = x² - 4x - 12

The factors that satisfy the sum of the middle term is - 6 + 2. Insert - 6x and + 2x into the equation.

0 = x² - 4x - 12

0 = x² - 6x + 2x - 12

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

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

- - - - - - -

Roots

x + 2 = 0

x + 2 - 2 = 0 - 2

x = - 2. . . .<=. .not used

- - - - - -

x - 6 = 0

x - 6 + 6 = 0 + 6

x = 6

The short leg = 6

The long leg = 8

The diagnol = 10

- - - - - - - - - s-

Answer 2

Short leg = x
Long leg = x + 2
Diagonal = Long leg + 2 = (x + 2) + 2 = x + 4

Since this is a right triangle, we can use the Pythagorean Theorem that tells us a² + b² = c², where a and b are the legs of the triangle, and c is the hypotenuse (or diagonal).

Set the short leg = a, the long leg = b, and the diagonal = c.

a² + b² = c²
(x)² + (x+2)² = (x+4)²
x² + (x² +4x +4) = (x² + 8x + 16)
2x² + 4x + 4 = x² + 8x + 16
x² - 4x -12 = 0
(x - 6)(x + 2) = 0

This tells us the short leg, x, can be either 6 or -2. Since its measurement really can't be negative, x = 6. So we have

short leg = x = 6
long leg = x + 2 = 8
diagonal = x + 4 = 10

Answer 3

Do you know your pythagorean theory?

The lengths of the triangle's sides are 6, 8, 10 I reckon.

Work out the rest, and try to learn the theory.. It is one of the mathematical ideas that is used regularly in real life. Tradesmen use it, for example brick layers, tilers - I'm sure there's others too.

Look it up, and study hard.

Answer 4

d = a+2
a = b+2 b = a-2
d*2 = a*2+b*2
(a+2)*2 = a*2 + (a-2)*2
a*2+4a+4 = a*2 + a*2-4a+4
a*2-8a =0
a(a-8)=0
a=8 b=6

Answer 5

Is that the whole problem? Not much info