On a recent test, Shawna was given the following problem:

A right triangle has side lengths 7 meters and a hypotenuse of 25 meters. The other side is labeled a.

Shawna's work is shown below:

1. a2+72=252

2. a2+14=50

3. a2=36

4. a=6 m

In which step did Shawna make an error?
Step 1. She incorrectly applied the Pythagorean theorem.
Step 2. She incorrectly squared the numbers.
Step 3. She incorrectly isolated a2
Step 4. She incorrectly solved for a.

Step 2. She incorrectly squared the numbers.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is