Question

halla las dimenciones de rectangulo sabiendo que su diagonal mide 22m y su area es de 231 m" .. ayudenme por faa plis

Answer 1

Sea:

a = Base

b = Altura

c = Diagonal

Area = ab

b = A/a

Por pitagoras

c² = a² + b²

c² = a² + A²/a²

a² + A²/a² = [(a²)(a²) + A²]/a²

c² = [(a²)(a²) + A²]/a²

a²c² = a^4  + A²

(a²)² - c²a² + A² = 0

Donde: a = 1;  b = -c²;  c = A²

$a^{2} =\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$a^{2} =\frac{-(-c^{2}) \pm \sqrt{(-c^{2}) ^2-4(1)(A^{2})}}{2(1)}$

$a^{2} =\frac{c^{2} \pm \sqrt{c^{4}-4A^{2}}}{2}$

Reemplazamos

A² = (231)² = 53361

c = 22; c² = 484; c^4 = 234256

$a^{2} =\frac{(484)\pm \sqrt{(234256)-4(53361)}}{2}$

$a^{2} =\frac{(484)\pm \sqrt{20812}}{2}$

$a^{2} =\frac{484\pm \ 144.2636475 }{2}$

a²(1) = [484 + 144.2636475]/2 = 314.1318238

a²(2) = [484 - 144.2636475]/2 = 169.8681763

a(1) = √314.1318238 = 17.72376438

a(2) = √169.8681763 = 13.03334862

Uso a(2) = 13.03334862

a = 13.03334862 m
 
b =A/a

b = 231/13.03334862

b = 17.72376438 m

Rta: Los lados son de 13.03334862 m  y 17.72376438 m