Question

ABC is a right-angled triangle with angle ABC = 90° ,BC = 12 cm ,AB = 15 cm and CD = 5cm. Find the length of BD and AD​

Answer 1

HEY

Here is your Answer:

In Triangle BDC

BD²= BC²+CD²

BD² = 12² + 5²

BD² = 144 +25

BD² = 169

BD = 13cm

In Triangle ABC

AB²= AC²  + BC²

15² =  AC² + 12²

225 = AC² + 144

AC² = 225 - 144

AC² = 81

AC = 9

We know that AC = AD + CD

SO,

9 = AD + 5

AD = 9-5

AD = 4

Answer 2

Step-by-step explanation:

In Right angle triangle BDC

(BD)

${bd}^{2} = {bc}^{2} + {cd}^{2}$

${ bd}^{2} = {12}^{2} + {5}^{2} \\ {bd}^{2} = 144 + 25 \\ {bd}^{2} = 169$

${bd}^{2} = {13}^{2} \\ sq \: cut \: from \: sq \\ bd \: = 13$

hence bd = 13

In right angle triangle BAD

${ba}^{2} = {bd}^{2} + {ad}^{2} \\ {15}^{2} = {13}^{2} + {ad}^{2} \\ 225 = 169 + {ad}^{2} \\ 225 - 169 = {ad}^{2} \\ 56 = {ad}^{2} \\ \sqrt{56 } = ad \: \\ 2 \sqrt{14} \: cm = ad$

hence

hence 2

$2\sqrt{14}$

is equal to Ad

hence done.

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