What is the area of the largest triangle that can be inscribed in the semicircle? One side of the triangle is the 10-unit diameter of the semicircle.

25 unit²

Step-by-step explanation:

The largest area triangle will have the largest height as the base is fixed at 2R

The largest height will be R

A = ½(2R)R = R²

A = (10/2)² = 25

the correct answer is 5 6 and 7

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4