Advertisements
Advertisements
प्रश्न
In ΔABC, DE is drawn parallel to BC cutting AB in the ratio 2 : 3. Calculate:
(i) `("area"(Δ"ADE"))/("area"(Δ"ABC")`
(i) `("area"("trapeziumEDBC"))/("area"(Δ"ABC"))`
उत्तर
AD : DB = 2 : 3
AB
= AD + DB
= 2 + 3
= 5
(i) `("area"(Δ"ADE"))/("area"(Δ"ABC")) = "AD"^2/"AB"^2`
⇒ `("area"(Δ"ADE"))/("area"(Δ"ABC")) = (2^2)/(5^2)`
⇒ `("area"(Δ"ADE"))/("area"(Δ"ABC")) = (4)/(25)`.
(ii) `("area"("trapeziumEDBC"))/("area"(Δ"ABC")) = ("area"(Δ"ABC") - "area"(Δ"ADE"))/("area"(Δ"ABC"))`
⇒ `("area"("trapeziumEDBC"))/("area"(Δ"ABC")) = (25 - 4)/(25)`
⇒ `("area"("trapeziumEDBC"))/("area"(Δ"ABC")) = (21)/(25)`.
APPEARS IN
संबंधित प्रश्न
In figure, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm, AP = 2.8 cm, find CA and AQ.
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles
O is any point in the interior of ΔABC. Bisectors of ∠AOB, ∠BOC and ∠AOC intersect side AB, side BC, side AC in
F, D and E respectively.
Prove that
BF × AE × CD = AF × CE × BD
The scale of a map is 1 : 200000. A plot of land of area 20km2 is to be represented on the map. Find:
The number of kilometres on the ground represented by lcm or the map
The dimensions of the model of a multistorey building are 1.2 m × 75 cm × 2 m. If the scale factor is 1 : 30; find the actual dimensions of the building.
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD = 4x - 3, AE = 8x - 7, BD = 3x - 1 and CE = 5x - 3,Find x.
In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that TP:TQ = TR:TS
Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y
If ΔABC ~ ΔLMN and ∠A = 60° then ∠L = ?
∆ABC ~ ∆PQR. If AM and PN are altitudes of ΔABC and ∆PQR respectively and AB2 : PQ2 = 4 : 9, then AM : PN = ______.
