Question

5. In a right triangle ABC, B = 90°
(a) If AB = 6 cm, BC = 8 cm, find AC.
(b) If AC = 13 cm, BC = 5 cm, find AE
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Answer 1

Answer:

AC=10 cm

AE=12cm

Step-by-step explanation:

By pythagoras theorem,

a)

${6}^{2} + {8 }^{2} = {ac}^{2} \\ 36 + 64 = {ac}^{2} \\ 100 = {ac}^{2} \\ ac = \sqrt{100} \\ ac = 10 \: cm$

b)

${5}^{2} + {ae}^{2} = {13}^{2} \\ 25 + {ae}^{2} = 169 \\ {ae}^{2} = 169 - 25 \\ {ae}^{2} = 144 \\ ae = \sqrt{144} \\ ae = 12 \: cm$

Hope it helps you out.....

Answer 2

Step-by-step explanation:

Given : (a) AB=6cm , BC=8cm and B=90°

here , AC = H , AB = P, BC = B

using Pythagoras theorm : H²=P²+B²

AC²= (6)²+(8)²

AC²=36+48

AB²AC=√84

AC=4√21cm

(b) Now, AC=13 cm , BC=5cm

using Pythagoras theorm

H²=P²+B²

AC²=AB²+BC²

(13)²=AB²+(5)²

169–25=AB²

√144=AB

AB=12cm

Hope this will help you ☜☆☞