Question 1006526
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<U>Problem 1</U>

Let n be an unknown integer.

Then you have an equation 

{{{n + 5n^2}}} = {{{174}}}, or

{{{5n^2 + n - 174}}} = {{{0}}}.

Solve it using the quadratic formula

{{{n[1,2]}}} = {{{(-1 +- sqrt(1 + 4*5*174))/10}}} = {{{(-1 +- 59)/10}}}.

The appropriate root is -6 (integer).


<U>Problem 2</U>

"A right triangle has a height 8 cm more than twice the length of the base. 
If the area of the triangle is 96 cm2, what are the dimensions of the triangle".
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I don't like this formulation very much.

When someone talks about a height of a right-angled triangle, he/she means the height drawn to the hypotenuse. 
When a right-angled triangle is considered, it is a BAD style to call the hypotenuse as "the base".  

From the other side, in a right triangle the height drawn to the hypotenuse CAN NOT be longer than half of the hypotenuse.
  (Remember, a right-angled triangle is inscribed into the circle, and the right angle is leaning on the diameter!)

Taking this into account, the condition seems very suspicious to me from the point of view whether terminology is using correctly.
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