civonamzuk

Points X, Y, and Z are on the sides QR, PR, and PQ respectively, of right triangle PQR  such that PZXY is a square. If PQ=12 and PR=8, then what is the side length of the square?

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Triangles PQR and ZQX are similar!

Square side => a

XZ / (PQ - PZ) = PR / PQ

a / (12 - a) = 8 / 12

a = 4.8

Let angle A = 90º

CE = 2

EA = 3

AD = 4

DB = 8

[ACD]/[ABE] = 5/9

In an isosceles △ABC (AC = BC) its incircle touches the side BC at point T. Given AC = 4 and AT = 3. Find the length of AB.

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AB < 4 and                ∠ATB < 90º 

BT = x            AB = 2x

AB = 3.271

The circle centered at (2,-1) and with radius 4 intersects the circle centered at (2,-5) and with radius sqrt(10) at two points A and B. Find (AB)²

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PR = 4         PQ = 4 - QR

(BP)² - (PQ)² = (BR)² - (QR)²

4² - (4 - QR)² = 10 - (QR)²

QR = 1¹/₄          (PQ = 2³/₄)

AB = 2{sqrt[(BR)² - (QR)²]}            

(AB)² = 33³/₄

You're absolutely right!!!

In order for them to have the same amount of money, Josh MUST give $28 to Ken!!!

But, in the following equation, Ken will "give" $28 to Josh!?!? It's weird!!! 

2/5x + 28 = 3/4x - 28

x = 160

Josh had $120              3/4(160) = 120        120 - 28 = 92        2/5(120) = 48

Ken had  $64                2/5(160) = 64           64 + 28 = 92         3/4(64) = 48

PQ = CQ = x         ∠PCQ = 45º         ∠PBQ = 30º

tan(45º) * x = tan(30º) * (4 - x)

x = 2(√3 -1) ≈ 1.464

An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters  What is the perimeter of the octagon?

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Square side = 1/4(108) = 27

Octagon perimeter = 8(27/3) = 72

Peter had 26 coins.

6 quarters

8 dimes

12 nickles