An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 9 inches, and the length of the base is 7 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.

P = 26.4 inches

Step-by-step explanation:

3.5² + 9² = c²

12.25 + 81 = c²

c² = 93.25

c = √93.25 ≈ 9.7

so 9.7 are the lengths of the sides opposite the congruent angles

P = 9.7(2) + 7

P =  19.4 + 7

P = 26.4 inches

26.3

Step-by-step explanation:

Delta math answer

english, cause i can’t you

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