SAT Triangle Maximum Area

For an SAT Math question that gives two sides of a triangle 7, 10.

You could pick any kind of triangle you want, but I would recommend thinking about a right triangle, if you do that, you don’t need to use any trig functions. And that is the type of triangle that it turns out will maximize the area.

It could help to sketch this out.

You also need to know the formula for the area of a triangle.

So I imagined the bass as 7 and the height as 10, you don’t need to know what the hypotenuse is.

So (7*10)/2 = 35, which is a possible choice.

You could get less area, but not more for the given dimensions.

The choices that are larger than 35 are much larger. 70 might reflect the mistake of not multiplying by 1/2.

I think it really comes down to knowing the equation for area of a triangle.