Question

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Answer 1

GỌI CẠNH

ngắn: x, x>0

DÀI: X+  30

ĐƯỜNG CHÉO $\sqrt{ x^{2} +(x+30)^{2} }$

$\sqrt{ x^{2} +(x+30)^{2} }$   =X+60

$x^{2} +(x+30)^{2}$=  $(x+60)^{2}$

$x^{2} =(x+60)^{2} -(x+30)^{2}$

$x^{2} =(x+60+x+30) * (x+60-x-30)$

$x^{2} = (2x+90)*30$

$x^{2} = 60x+2700$

$\left \{ {{x_{1} =90} \atop {x_{2} _=(-30)}} \right.$

suy ra

x =9 0

nên

ngắn =90m

dài=120m

ĐƯỜNG CHÉO: $\sqrt{90^{2} +120^{2} }$=150