Question

Can somebody please help me with these two questions? And show your work please?

Answer 1

(1)   x = 12,   (2)   $x=3\frac{1 }{2}$

Solution:

(1)     If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.

⇒ $\frac{25}{10}=\frac{30}{x}$

Do cross multiply.

⇒ $25 \times x=30 \times 10$

Divide both sides of the equation by 25 to equal the expression.

⇒ $x=\frac{30 \times 10}{25}$

⇒ x = 12

(2)   Side of triangle = $4\frac{1}{3} =\frac{13}{3}$

If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.

⇒ $\frac{26}{\frac{13}{3} }=\frac{21}{x}$

Do cross multiply.

⇒ $26 \times x=21 \times \frac{13}{3}$

⇒ $26 \times x=7 \times 13$

Divide both sides of the equation by 26 to equal the expression.

⇒ $x=\frac{7 \times 13}{26}$

⇒ $x=\frac{7 }{2}$

⇒ $x=3\frac{1 }{2}$