Question

Calculate the length of -
1. AB
2. BC

(2) Prove that triangle ABC is right angled.

Plz... Give the right answer only. Plz...​

Answer 1

${\huge{\underline{\sf {\pink{Answer}}}}}$

AB = 45 cm

BC = 60 cm

$\: \:$

${\huge{\underline{\sf {\pink{Explanation :}}}}}$

GIVEN :

BD = 36 cm

AD = 37 cm

CD = 48 cm

$\angle ADB$ = 90°

$\angle BDC$ = 90°

$\: \: \:$

FORMULA :

We know in a right angle triangle,

${h}^{2} = {p}^{2} + {b}^{2}$

where,

h = hypotenuse

p = perpendicular

b = base

$\: \: \:$

Solution :

Part 1 :

In ∆BDC, BC is the hypotenuse

${h}^{2} = {p}^{2} + {b}^{2}$

${BC}^{2} = {BD}^{2} + {CD}^{2}$

${BC}^{2} = {36}^{2} + {48}^{2}$

${BC}^{2} = 1296 \: + \: 2304 \\ = 3600$

$BC = \sqrt{3600} \\ = 60 \: cm$

$\: \: \:$

Again,

In ∆ABD, AB is the hypotenuse,

${AB}^{2} = {BD}^{2} + {AD}^{2}$

${AB}^{2} = {36}^{2} + {27}^{2}$

${AB}^{2} = 1296 \: + \: 729 \\ = 2025$

$AB \: = \sqrt{2025} \\ = 45 \: cm$

$\: \: \: \:$

Part 2 :

AB = 45 cm

BC = 60 cm

AC = (27 + 48) cm = 75 cm

${AB}^{2} = {45}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2025$

${BC}^{2} = {60}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3600$

${AC}^{2} = {75}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5625$

We can see,

$2025 + 3600 = 562 \\ {AB}^{2} + {BC}^{2} = {AC}^{2}$

So,

here AC is the hypotenuse,

with $\angle B$ = 90°

--- Proved

Answer 2

Answer:

both answers are correct thank you

Step-by-step explanation:

From class 8