In the figure,ABCD is a rectangle. G is a point on CD. The area of the triangle AGH is 7 square centimeters and the area of the triangle BGH is 4 square centimeters.
a)what is the area of the triangle AGD?
b)what is the area of the triangle BGC?
c)what is the area of the triangle ABG?
d)what is the area of the rectangle ABCD?
e)what is the relation between the area of the triangle ABG and that of the rectangle ABCD?
Answers
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Step-by-step explanation:
Using Pythagoras theorem in right triangle ABC, we obtain
AC
2
=AB
2
+BC
2
⇒(5+2)
2
+(2−t)
2
={(5−2)
2
+(2+2)
2
}+{(2+2)
2
+(−2−t)
2
}
⇒49+(4−4t+t
2
)=(9+16)+(16+4+4t+t
2
)
⇒t
2
−4t+53=t
2
+4t×45
⇒−8t=−8
⇒t=1
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