# Simple Geometry. Find x.?

### 5 Answers

- PuzzlingLv 79 months agoFavourite answer
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

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- JOHNLv 79 months ago
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.

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- Steve ALv 79 months ago
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.

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- Anonymous9 months ago
I have no exes..........

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- MarkLv 79 months ago
If it's so simple, then why don't you do it yourself? I'll give you a hint: think right triangle and the Pythagorean Theorem.

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