Answer the 10th question { NO LINKS } { NO ANSWERS FROM GOOGLE } : 10 ABC - Maths - Area Theorems

Question

Answer the 10th question { NO LINKS } { NO ANSWERS FROM
GOOGLE } :

10 ABC is a triangle in which AB=AC=4 cm and ∠ A = 90 °
Calculate the area of △ ABC Also find the length of
perpendicular from A and BC
Hint: By Pythagoras theorem,
BC2=AB2+AC2=42+42=32
⇒ BC =4 2 cm

Surabhi Grover · Accepted Answer

Dear Student,
Consider the figure:

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_59e86ea848df8%20jpg"
style="width: 250px; height: 199px;">
Area (∆ABC)=12(AC)(AB)=12×4×4=8cm2Applying pythagoras theorem in∆ABCBC2=AB2+AC2⇒BC2=16+16=32cm2So, BC=42cmLet AD be the perpendicular from A to BC)Consider ∆ADC and∆ADB∠D=90° (AD is perpendicular)AC=AB=4cm (Given)∠B=∠C (Angles opposite to same sides of a triangle are equal)So∆ADC ≅∆ADB (By AAS critera)So DC=DB=422=22cm⇒AD=AC2-DC2 (By pythagoras theorem)⇒AD=16-8=22cm
Regards

Answer the 10th question. { NO LINKS }.{ NO ANSWERS FROM GOOGLE }.: 10. ABC is a triangle in which AB=AC=4 cm and ∠ A = 90 ° . Calculate the area of △ ABC. Also find the length of perpendicular from A and BC. Hint: By Pythagoras theorem, BC2=AB2+AC2=42+42=32 ⇒ BC =4 2 cm.