Question

0 multiple choice 2 points two triangles are similar. the measure of the shortest side of the first triangle is 12 and the measure of the shortest side of the second triangle is 5. if the longest side of the first triangle measures 15, what is the measure of the longest side of the second triangle? 6.25 36 2.4 24 1 multiple choice 2 points jennies math tutor drew three lines to create a right angle scalene triangle in her math notebook. which of the following are the possible whole number lengths of the three segments? 7,24,25 16,17,23 2,3,4 33,35,48 2 multiple choice 2 points what is the measure of the largest angle in the accompanying triangle? (2x + 1)° (x + 15)° x° 56 46.5 83 41

Explanation:

Question 0

Step1: Set up similarity proportion

$\frac{\text{Short side 1}}{\text{Short side 2}} = \frac{\text{Long side 1}}{\text{Long side 2}}$
$\frac{12}{5} = \frac{15}{x}$

Step2: Solve for $x$

$x = \frac{15 \times 5}{12} = 6.25$

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Question 1

Step1: Check Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$

Step2: Test [7,24,25]

$7^2 + 24^2 = 49 + 576 = 625 = 25^2$

Step3: Eliminate other options

$16^2+17^2=256+289=545
eq 23^2=529$; $2^2+3^2=4+9=13
eq 4^2=16$; $33^2+35^2=1089+1225=2314
eq 48^2=2304$

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Question 2

Step1: Sum of triangle angles

$(2x+1) + (x+15) + x = 180$

Step2: Simplify and solve for $x$

$4x + 16 = 180$
$4x = 164$
$x = 41$

Step3: Calculate largest angle

Largest angle is $2x+1 = 2(41)+1 = 83$

Answer:

6.25