# Triangle A has an area of 12  and two sides of lengths 5  and 7 . Triangle B is similar to triangle A and has a side with a length of 19 . What are the maximum and minimum possible areas of triangle B?

Maximum Area $= 187.947 \text{ }$square units
Minimum Area $= 88.4082 \text{ }$square units

#### Explanation:

The triangles A and B are similar. By ratio and proportion method of solution, triangle B has three possible triangles.

For Triangle A: the sides are

$x = 7$, $y = 5$, $z = 4.800941906394$,Angle $Z = {43.29180759327}^{\circ}$

The angle Z between sides x and y was obtained using the formula for area of triangle

$A r e a = \frac{1}{2} \cdot x \cdot y \cdot \sin Z$

$12 = \frac{1}{2} \cdot 7 \cdot 5 \cdot \sin Z$

$Z = {43.29180759327}^{\circ}$

Three possible triangles for Triangle B: the sides are

Triangle 1.
${x}_{1} = 19$, ${y}_{1} = \frac{95}{7}$,${z}_{1} = 13.031128031641$,
Angle ${Z}_{1} = {43.29180759327}^{\circ}$

Triangle 2.
${x}_{2} = \frac{133}{5}$,${y}_{2} = 19$, ${z}_{2} = 18.243579244297$,
Angle ${Z}_{2} = {43.29180759327}^{\circ}$

Triangle 3.
${x}_{3} = 27.702897180004$, ${y}_{3} = 19.787783700002$,
Angle ${Z}_{3} = {43.29180759327}^{\circ}$

Maximum Area with Triangle 3.
Minimum Area with Triangle 1.

God bless....I hope the explanation is useful.