Advertisements
Advertisements
Question
In Fig. below, triangle ABC is right-angled at B. Given that AB = 9 cm, AC = 15 cm and D,
E are the mid-points of the sides AB and AC respectively, calculate
(i) The length of BC (ii) The area of ΔADE.
Advertisements
Solution
In right ΔABC, ∠B = 90°
By using Pythagoras theorem
`AC^2 = AB^2+ BC^2`
⇒ `15^2 = 9^2 +BC^2`
⇒ BC =`sqrt(15^2 - 9^2)`
⇒ BC =`sqrt(225-81)`
⇒ BC =`sqrt144`
= 12cm
In ΔABC
D and E are midpoints of AB and AC
∴ DE || BC, DE = `1/2` BC [By midpoint theorem]
AD = OB = `(AB)/ 2= 9/2` = 4 . 5cm [ ∵ D is the midpoint of AB]
DE = `(BC)/2 = 12/2` = 6cm
Area of ΔADE = `1/2 xxAD xx DE `
= `1/2× 4 .5 × 6 = 13.5cm^2`
APPEARS IN
RELATED QUESTIONS
In below fig. ABCD is a parallelogram and E is the mid-point of side B If DE and AB when produced meet at F, prove that AF = 2AB.
In ∆ABC, E is the mid-point of the median AD, and BE produced meets side AC at point Q.
Show that BE: EQ = 3: 1.
In triangle ABC, AD is the median and DE, drawn parallel to side BA, meets AC at point E.
Show that BE is also a median.
ABCD is a quadrilateral in which AD = BC. E, F, G and H are the mid-points of AB, BD, CD and Ac respectively. Prove that EFGH is a rhombus.
In a right-angled triangle ABC. ∠ABC = 90° and D is the midpoint of AC. Prove that BD = `(1)/(2)"AC"`.
ABCD is a parallelogram.E is the mid-point of CD and P is a point on AC such that PC = `(1)/(4)"AC"`. EP produced meets BC at F. Prove that: F is the mid-point of BC.
In ΔABC, X is the mid-point of AB, and Y is the mid-point of AC. BY and CX are produced and meet the straight line through A parallel to BC at P and Q respectively. Prove AP = AQ.
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC ⊥ BD. Prove that PQRS is a rectangle.
Prove that the line joining the mid-points of the diagonals of a trapezium is parallel to the parallel sides of the trapezium.
