Need help! Given the length of rectangle is 3m longer than breathe and diagonal of rectangle is 17m. Area?

Answer 1

Length = L = Width + 3 = W + 3

L, W and the diagonal form a right triangle so you can use:
c^2 = a^3 + b^2.

Let a = W and b = L = W + 3, then:
(17)^2 =W^2 + (W + 3)^2
289 = W^2 + W^2 + 6W + 9
W^2 + 3W - 140 = 0

The quick way is to note that:
W^2 + 3W = 140
And that:
Area = W*L = W*(W + 3)
And W^2 + 3W = W*(W + 3) .... above equation
So Area = 140

If you want detailed calculation:
W = (-3 +/- SQRT(9 + 560))/2
W = (-3 + SQRT(569))/2 The negative one is not needed
W = 10.43 and L = 13.43

Area = W*L = 140 m^2

Answer 2

The breadth is 3, the length then is 3 + x. Use the Pythagorean theorem:

x^2 + (x + 3)^2 = 17^2
x^2 + x^2 + 6x + 9 = 289
2x^2 + 6x + 9 =289
2x^2 + 6x - 280 = 0
Using quadratic formula, x = 10.426 and -13.426
Disregard the negative answer.
So the dimensions are 10.426m by 13.426 m and the area is about 10.426m * 13.426m = 139.98 sq m

Answer 3

b-a=3; a^2+b^2=289

a^2+a^2+6a+9=289

2a^2+6a-280=0

a^2+3a-140=0

solve this for answer