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3 years ago

Please help with geometry homework ! Mark brainliest

Mathematics

1 answer:

GrogVix [38]3 years ago

5 0

<u>Answer</u>

<u>Explanation</u>

The product of the secant and the extension of the chord is normally equivalent to square of the tangent.

From the diagram given,

The length of the secant = 2+6

= 8

Length of the extension of the chord = 6

length of the tangent = x

∴ x² = 8 × 6

= 48

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Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

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Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

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$\frac{20}{x/2} = \frac{x + 34}{1775}$

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Cross multiply

$x *(x + 34) = 1775 * 40$

Open bracket

$x^2 + 34x = 71000$

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$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

$x - 250 = 0 \ or\ x + 284= 0$

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So:

$x = 250$

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