Respuesta :
Given:
The legs of a right triangle are 8 cm and 12 cm.
The hypotenuse of a similar triangle is 20 cm.
To find:
The area of the larger triangle.
Solution:
According to the Pythagoras theorem,
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
The legs of a right triangle are 8 cm and 12 cm.
[tex]hypotenuse^2=(8)^2+(12)^2[/tex]
[tex]hypotenuse^2=64+144[/tex]
[tex]hypotenuse^2=208[/tex]
Taking square root on both sides.
[tex]hypotenuse=\sqrt{208}[/tex]
[tex]hypotenuse=4\sqrt{13}[/tex]
The hypotenuse of a similar triangle is 20 cm. So, scale factor is
[tex]k=\dfrac{20}{4\sqrt{13}}[/tex]
[tex]k=\dfrac{5}{\sqrt{13}}[/tex]
So, legs of larger triangle are
[tex]8\times \dfrac{5}{\sqrt{13}}=\dfrac{40}{\sqrt{13}}[/tex]
[tex]12\times \dfrac{5}{\sqrt{13}}=\dfrac{60}{\sqrt{13}}[/tex]
Area of triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
[tex]A=\dfrac{1}{2}\times \dfrac{40}{\sqrt{13}}\times \dfrac{60}{\sqrt{13}}[/tex]
[tex]A=\dfrac{2400}{2(\sqrt{13})^2}[/tex]
[tex]A=\dfrac{1200}{13}[/tex]
[tex]A=92.30769[/tex]
[tex]A\approx 92.31[/tex]
Therefore, the area of the larger triangle is about 92.31 sq cm.
