Advertisements
Advertisements
प्रश्न
Figure shows Δ PQR in which ST || QR and SR and QT intersect each other at M. If `"PT"/"TR" = 5/3` find `("Ar" (triangle "MTS"))/("Ar" (triangle "MQR"))`
उत्तर
Given : `"PT"/"TR" = 5/3`
To find : `("Ar" (triangle "MTS"))/("Ar" (triangle "MQR"))`
Sol : In Δ PST and Δ PRQ
∠ PST = ∠ PQR
∠ PST = ∠ PQR ...(Corresponding angles)
∴ Δ PST ∼ Δ PQR ....(AA corollary)
∴ `"PT"/"PR" = "ST"/"QR" = 5/8` .....(similar sides of similar triangles)
Now, In Δ MTS and Δ MQR
∠ MTS = ∠ MQR ...(Alternate interior angles)
∠ MTS = ∠ MQR
∴ Δ MTS ∼ Δ MQR ....(AA corollary)
`therefore ("Ar" (triangle "MTS"))/("Ar" (triangle "MQR")) = "TS"^2/"QR"^2 = (5/8)^2 = 25/64`
i.e. 25 : 64
[The ration of areas of two similar triangle is equal to the ratio of square of their corresponding sides.]
APPEARS IN
संबंधित प्रश्न
In a triangle ABC, line l || Side BC and line l intersects side AB and AC in points P and Q, respectively. Prove that: `"AP"/"BP"="AQ"/"QC"`
P and Q are points on the sides AB and AC respectively of a ΔABC. If AP = 2cm, PB = 4cm, AQ = 3cm and QC = 6cm, show that BC = 3PQ.
In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.
ΔABC ∼ ΔDEF and A(ΔABC) : A Δ(DEF) = 1 : 2 If AB = 4 find DE.
Find the scale factor in each of the following and state the type of size transformation:
Actual area = 64m2, Model area = 100cm2
On a map drawn to a scale of 1: 2,50,000, a triangular plot of land has the following measurements:
AB = 3 cm, BC = 4 cm, ∠ABC = 90°. Calculate:
(i) The actual length of AB in km.
(ii) The area of Plot in sq. km.
The dimensions of the model of a building are 1.2m x 75cm x 2m. If the scale factor is 1 : 20; find the actual dimensions of the building.
A model of cargo tuck is made to a scale of 1:40. The length of the model is 15cm. Calculate: The length of the truck
From the figure, prove that ∆SUN ~ ∆RAY
ΔABC ~ ΔPQR, A(ΔABC) = 80 sq.cm, A(ΔPQR) = 125 sq.cm, then complete `("A"(Δ"ABC"))/("A"(Δ"PQR")) = 80/125 = (["______"])/(["______"])`, hence `"AB"/"PQ" = (["______"])/(["______"])`
