In δabc, ac = bc, cd ⊥ ab with d ∈ ab , ab = 4 in, and cd = sqrt3 in. find ac.

The length of AC is inches.

Given in ΔABC, AC = BC it shows that ΔABC is an isosceles triangle.

The length of AB is 4 inches and the length of CD is inches.

Since CD is perpendicular to AB, so the ΔABC is divided in two right angled triangle namely ΔADC and ΔBDC.

We have to find the length of AC, so we consider right triangle ADC here.

We know that in right angled triangle,The Pythagoras Theorem states that the sum of the square of the base and square of the perpendicular is equal to the square of the hypotenuse.

So ......equation 1.

In an isosceles triangle the perpendicular drawn from the vertex always bisect the base since here CD ⊥ AB so AD = BD = half of AB = 2.

Now putting the values in equation 1 we get,

Hence the length of AC is inches.

For more details on Pythagoras theorem follow the link below:

link

step-by-step explanation:

if x = 2 you have to find x to finish the problem