Question

Aflati lungimile catetelor unui triunghi dreptunghic, dacă inaltimea triungh
unghiului drept imparte ipotenuza in două segmente cu lungimile de:
a) 6 cm si 24 cm;
b) 12 cm şi 16 cm;
8 cm si 10 cm:
va rog

Answer 1

 

Aplicam teorema catetei care spune:

Intr-un triunghi dreptunghic patratul catetei este egal cu produsul dintre ipotenuza si proiectia ei pe ipotenuza

.

$\displaystyle\bf\\a)\\c_1=\sqrt{6\times(6+24)}=\sqrt{6\times30}=\sqrt{180}=\sqrt{36\times5}=\boxed{\bf6\sqrt{5}}\\\\c_2=\sqrt{24\times(6+24)}=\sqrt{24\times30}=\sqrt{720}=\sqrt{144\times5}=\boxed{\bf12\sqrt{5}}\\\\\\b)\\c_1=\sqrt{12\times(12+16)}=\sqrt{12\times28}=\sqrt{336}=\sqrt{16\times21}=\boxed{\bf4\sqrt{21}}\\\\c_2=\sqrt{16\times(12+16)}=\sqrt{16\times28}=\sqrt{448}=\sqrt{64\times7}=\boxed{\bf8\sqrt{7}}$

.

$\displaystyle\bf\\c)\\c_1=\sqrt{8\times(8+10)}=\sqrt{8\times18}=\sqrt{144}=\boxed{\bf12}\\\\c_2=\sqrt{10\times(8+10)}=\sqrt{10\times18}=\sqrt{180}=\sqrt{36\times5}=\boxed{\bf6\sqrt{5}}$