Question

Triangle abc a=90.And ad perpendicular to bc where d lies on bc.If bc eaual to 8 ac equal 6 then abc: acd

Answer 1

Answer:

9:5

Step-by-step explanation:

Given ∠BAC = 90°, BC = 8 cm, AC = 6 cm.

Let DC = y cm

Using Pythagoras theorem,

AB² + AC² = BC²

=> AB = √(8)² - (6)² = √28 = 2√7 cm.

∠BCA = x , ∠CAD = 90-x

=> ∠BAD = x, ∠ABD = 90-x

ΔABC, ΔADC and ΔABD are similar triangles.

AC/AB = BD/DC

6/2√7 = 8-y/y

3/√7 = 8-y/y

3y = 8√7 - √7 y

y = 8√7/3+√7  = 4√7(3-√7) = 12√7 - 28 = 3.75 cm.

BD = 8 -3.75 = 4.25 cm

ΔADC is right angled triangle,

AD² + DC² = AC²

AD = 4.68 cm.

Area of ΔABC = 1/2*AC*AB = 1/2*6*2√7 = 6√7 cm² = 15.88 cm²

Area of ΔACD = 1/2*3.75*4.68 = 8.775 cm²

ΔABC:ΔACD  = 15.88: 8.78 = 1.8 : 1 = 9:5