Question

Plz help need explanation not answers:)

Draw one right triangle with side lengths labeled, to fit all of the statements below.

1). 60 is the geometric mean of 36 and 100.

2). 80 is the geometric mean of 64 and 100.

3). 48 is the geometric mean of 36 and 64.

Answer 1

Let ABC a right triangle in A (BC is the hypotenuse).

From A, draw the altitude AH, intersecting the hypotenuse in H
In any right triangle , the square of the altitude AH is equal to BH x HC, then

AH² = BH x HC
60² = 36 x 100 = 3600 So BH = 36 and HC = 100 (and the altitude = 60)

Follow the same logic for the remaining questions.

NB ( you can easily demonstrate that AH² = BH x HB, if you notice that the right triangles ABH and CAH are similar)

AH is called the geometric mean