Question

please help me solve these problems
find the length of the missing side​

Answer 1

$( \sqrt{21) {}^{2} } = 3 {}^{2} { + p}^{2}$

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

21=9+p^2

21-9=p^2

/12=p

p =a

Answer 2

Answer:

6. a = 2 root3 & 7. c = 2 root6

Step-by-step explanation:

6.

Given: In right-angled triangle h = root under 21 & b = 3 & p = a

Solution:

We know that in right-angled triangle

${h}^{2} = {b}^{2} + {p}^{2} \\ = > { (\sqrt{21} )}^{2} = {3}^{2} + {a}^{2} \\ = > 21 = 9 + {a}^{2} \\ = > {a}^{2} = 21 - 9 \\ = > {a }^{2} = 12 \\ = > a = \sqrt{12} \\ \: \: \: \: \: \: a = 2 \sqrt{3}$

7.

Given: In right-angled triangle b=root under 11, p = root under 13 & h = c

Solution:

As we know,

${h}^{2} = {b}^{2} + {p}^{2} \\ = > {c}^{2} = { (\sqrt{11} )}^{2} + { (\sqrt{13}) }^{2} \\ = > {c }^{2} = 11 + 13 \\ = > {c}^{2} = 24 \\ = > c = \sqrt{24} \\ \: \: \: \: \: \: \: c = 2 \sqrt{6}$