Question

In a triangle ABC, right angle is at point C, mBC =2.1cm and mAC =7.2cm. What is the length of AB.

Answer 1

Answer:

The length of AB is 7.5 cm

Step-by-step explanation:

In a right-angled triangle $\triangle ABC$, by Pythagoras theorem,

$AB^2=AC^2+BC^2$

where AB is the hypotenuse and AC and BC are other sides of the triangle.

Since the right angle in the given triangle is at  point C, the hypotenuse will be AB. Also given that

$mBC=2.1 \ cm\\mAC=7.2\ cm$

Thus, using the Pythagoras theorem, we have

$AB^2=2.1^2+7.2^2=4.41+51.84=56.25\\\\\implies AB=\sqrt{56.25}= 7.5\ cm$

Hence the length of AB is 7.5 cm.

Answer 2

(Pythagoras Theorem)

Formulas= Hypotenuse^2 = Base^2 + Altitude^2 (height)
                  Base^2 = Hypotenuse^2 - Altitude^2
                 Altitude^2 = Hypotenuse^2 - Base^2

So,
      We need to find the hypotenuse, that means
     
      H^2= B^2 + A^2
      H^2= (2.1)^2 + (7.2)^2
      H^2= 4.41 + 51.84
      H^2= 56.25
      H^2 = 7.5cm.  (Factorized)