Question

Triangle ABC is  right angled at vertex A. Calculate the length of BC, if AB = 15 cm and AC = 20 cm.

Select from the Answers below

13 cm 

 

21 cm 

 

25 cm



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Answer 1

Answer:

$\huge\mathfrak{\red{Answer}}$

$\rightarrow\small\bf BC \: = \: 25cm$

Step-by-step explanation:

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Question:-}}\mid}}}}$

• Triangle ABC is  right angled at vertex A. Calculate the length of BC, if AB = 15 cm and AC = 20 cm.

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Hint:-}}\mid}}}}$

• To find the lenght of BC; we will use the Pythagoras theorem in the ∆ ABC which is right angled at / A .

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Pythagoras \ theorem:-}}\mid}}}}$

• In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Required \ Solution:-}}\mid}}}}$

☆ Given:-

• A ∆ ABC where / A = 90°
• AB = 15 cm
• AC = 20 cm

☆ To find:-

• Length of BC.

By Pythagoras theorem we have;

${H}^{2} = {B}^{2} + {P}^{2}$

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

${BC}^{2} = {15}^{2} + {20}^{2}$

${BC}^{2} = 225 + 400$

$BC = \sqrt{625}$

$BC = \sqrt{ {25}^{2} }$

$BC = 25cm$

$\fbox{\purple{ BC \ = \ 25cm}}$

$\mathfrak{\red{ \ \ \ \ \ \ \ \ \ \ \ \ @MissTranquil}}$

Answer 2

$\huge \tt Given :$

• In ∆ABC is right angled triangle at vertex A.
• Length of AB= 15cm and AC = 20 cm.

$\huge \tt Find :$

• Calculate the length of BC.

$\huge \tt Theorem \: used :$

• In the right angled triangle the square of the hypotenuse side is equal to the sum of squares of other two sides.
• $\rightarrow\tt {hypo }^{2} = {height}^{2} + {base}^{2}$

$\huge \tt Solution :$

Here vertex is A.

$\tt\therefore\: {BC}^{2} = {AB}^{2} + AC$

$\tt \rightarrow{BC}^{2} = {15}^{2} + {20}^{2}$

$\tt \rightarrow \: {BC}^{2} = 225 + 400$

$\rightarrow \tt \: {BC}^{2} = 625$

$\tt \rightarrow \: {BC} = \sqrt{625}$

$\tt \rightarrow \fbox {\tt \green{ BC = 25}}$

Length of the BC is 25 cm.