(1) x = 12, (2) [tex]x=3\frac{1 }{2}[/tex]
Solution:
(1) If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.
⇒ [tex]\frac{25}{10}=\frac{30}{x}[/tex]
Do cross multiply.
⇒ [tex]25 \times x=30 \times 10[/tex]
Divide both sides of the equation by 25 to equal the expression.
⇒ [tex]x=\frac{30 \times 10}{25}[/tex]
⇒ x = 12
(2) Side of triangle = [tex]4\frac{1}{3} =\frac{13}{3}[/tex]
If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.
⇒ [tex]\frac{26}{\frac{13}{3} }=\frac{21}{x}[/tex]
Do cross multiply.
⇒ [tex]26 \times x=21 \times \frac{13}{3}[/tex]
⇒ [tex]26 \times x=7 \times 13[/tex]
Divide both sides of the equation by 26 to equal the expression.
⇒ [tex]x=\frac{7 \times 13}{26}[/tex]
⇒ [tex]x=\frac{7 }{2}[/tex]
⇒ [tex]x=3\frac{1 }{2}[/tex]