Martinez39:


X = (17 + 4√14)^½ ≈ 4.68685711 units.

ifada123:

Try again sir

Martinez39:
I will wait for your solution.

ifada123:

Try again sir

Martinez39:


Cc. Ifada123

Calculator error.

X = (17 + 4√14)½ ≈ 5.65390392 units.

ifada123:

Correct now,
Show full workings

Martinez39:
The number (17 + 4√14)½ is exactly what I posted before but I pressed wrongly on my calculator and got an inaccurate decimal approximation. I will post my workings soon.

Martinez39:
NB: I don't know basic geometry too well like ifada123 so I used coordinate geometry.

1) label the bottom left vertex, the bottom right vertex, top left vertex and top right vertex as A, B, C and D respectively.

2) Place the square on a coordinate plane with A at the origin, AB on the positive x-axis and AC on the positive y-axis. Hence the coordinates of the vertices are A(0, 0), B(x, 0), C(0, y) and D(x, y). Let the coordinates of the intersection point H in the square be (a, b). Observe that |AB| = |AC| since they are sides of a square. Therefore x = y.

3) Using the distance formula, we have
|HA|² = a² + b² = 5² = 25
|HB|² = (a - x)² + b² = 4² = 16
|HD|² = (a - x)² + (b - y)² = 3² = 9

Expanding, substituting and using the fact that x = y, we
have :
a = (x² + 9)/2x and b = (x² + 7)/2x.
Since a² + b² = 25, substitute and solve for x.
You will get an equation quadratic in form, which is x⁴ - 34x² + 65 = 0. Using the quadratic formula, x² = 17 ± 4√14. The value 17 - √14 yields an area for the square which is too small to contain the line segments hence

x = (17 + 4√14)½ ≈ 5.65390392 units.

Darivie04:
@ifada123 can you suggest books or sites containing practice problems on shapes?

femi4:
x² = 41 -40cosa


x² = 25 - 24cos b

Cos a = (41-x²)/40


Cos b = (25-x²)/24

40 cosa -24 cosb = 16

5 cosa - 3 cosb = 2


Also, (x√2)² = 5²+3² - 30 cos (360 - (a+b))
X² = 31 - 30 cos (a+b)
X² = 31 - 30 cosa cosb - sina sinb

Darivie04:
@ifada123 can you suggest books or sites containing practice problems on shapes?

ifada123:

I remember a friend told me of an app some years ago, that u subscribe and they teach u shape, but I did not take him serious then, because I prefer attempting it myself,
But I will ask him to give more details about it,
If u are interested, or if that's is what you think u need