Question

find AD if angle acd=60° ac=bc ab=100 m and angle adc=90°​

Answer 1

Answer:

In the triangle ABC, AB= 60, CA = 80 and BC = 100. D is a point on BC such that triangles ADB and ADC have equal perimeters. What is AD?

From the lengths given ABC is a right angled triangle with BC as the hypotenuse.

Let BD =x and CD = 100-x.

Equating the perimeters of triangles ADB and ADC we get 60+x+AD = 80+(100-x)+AD, or

60+x=180-x, or

2x = 120 or x = 60. Hence BD = 60.

In triangle ADB, AD^2 = AB^2+BD^2–2*AB*BD*cos <ABD

AD^2 = 60^2+60^2–2*60*60*(60/100) = 3600+3600–4320 = 2880, or AD = 2880^0.5 = 53.66563146 units.

Check: Perimeter of ABD = 60+60+53.66563146 = 173.6656315 units.

Perimeter of ACD = 80+40+53.66563146 = 173.6656315 units. Correct.

AD = 53.66563146 units.

Answer 2

Answer:

In the triangle ABC, AB= 60, CA = 80 and BC = 100. D is a point on BC such that triangles ADB and ADC have equal perimeters. What is AD?

From the lengths given ABC is a right angled triangle with BC as the hypotenuse.

Let BD =x and CD = 100-x.

Equating the perimeters of triangles ADB and ADC we get 60+x+AD = 80+(100-x)+AD, or

60+x=180-x, or

2x = 120 or x = 60. Hence BD = 60.

In triangle ADB, AD^2 = AB^2+BD^2–2*AB*BD*cos <ABD

AD^2 = 60^2+60^2–2*60*60*(60/100) = 3600+3600–4320 = 2880, or AD = 2880^0.5 = 53.66563146 units.

Check: Perimeter of ABD = 60+60+53.66563146 = 173.6656315 units.

Perimeter of ACD = 80+40+53.66563146 = 173.6656315 units. Correct.

AD = 53.66563146 units.

Step-by-step explanation: