Question

Triangle PQR is right angled which is right angled at the vertex C. AB=5
BC=4
AB=?

Answer 1

Answer:

Step-by-step explanation:

∵ Triangle ABC is right angled which is right angled at the vertex C

∴ AB is the hypotenuse , and BC is the adjacent as shown in the figure below

∵ AC² = AB² - BC²

∵ AB=5 , BC=4

∴ AC = $\sqrt{AB^{2} - BC^{2} }$

∴ AC = $\sqrt{5^{2} - 4^{2} }$

∴ AC = 3  

Answer 2

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1){\large\bf\5}\put(.3,2.5){\large\bf ?}\put(2.8,.3){\large\bf 4}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf C}\put(5.8,.3){\large\bf B}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf }\end{picture}$

Given -

• AB = 5
• BC = 4

To find -

• AC

Solution :-

By applying Pythagoras theorem -

➩ $\sf AC^2 + BC^2 = AB^2$

➩ $\sf AC^2 + 4^2 = 5^2$

➩ $\sf AC^2 + 16 = 25$

➩ $\sf AC^2 = 25 - 16$

➩ $\sf AC^2 = 9$

➩ $\sf AC = 3$