Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Simple Geometry. Find x.? Relevance

First, if the sides are x, we can agree the pink shape is a square. Its diagonal will be x√2

If this isn't clear, use the Pythagorean Theorem:

d² = x² + x²

d² = 2x²

d = √(2x²)

d = (√2)x

d = x√2

Now look what we can do in the diagram below. We can extend the bottom line by 9 more to make it 23. Then add a perpendicular line of 7 units. You have now formed a right triangle with legs of 7 and 23. The hypotenuse is also the diagonal of the square.

d² = 7² + 23²

d² = 578

d = √578

d = √289 * √2

d = 17√2

We can easily see that x = 17

d = x√2

d = 17√2

Hence:

x = 17 • Let u = ∠ length 14 segment makes with side of square.

Vertical side x has 3 parts:

x = 14sinu + 7cosu + 9sinu = 23sinu + 7cosu

Horizontal side x has 3 parts:

x = 14cosu + 7sinu + 9cosu = 23cosu + 7sinu

23sinu + 7cosu = 23cosu + 7sinu

16sinu = 16cosu

tanu = 1 (0 < u < 90)

u = 45

x = (23 + 7)/ √2 = 15√2.

• A diagonal.from upper right to lower left will form two similar right triangles with sides 14, y, √(196 + y^2) and 9, 7-y, √(81 +(7-y)^2)

14/y = 9/(7-y)

98 -14y = 9y

y = 98/23

Should be easy from there since both sides are the same.

• Anonymous
1 month ago

I have no exes..........