Advertisements
Advertisements
प्रश्न
Figure shows Δ KLM , P an T on KL and KM respectively such that∠ KLM =∠ KTP.
If `"KL"/"KT" = 9/5` , find `("Ar" triangle "KLM")/("Ar" triangle "KTP")`.
उत्तर
Given : `"KL"/"KT"= 9/5`
To find : `("Ar" triangle "KLM")/("Ar" triangle "KTP")`
Sol : In Δ KLM and Δ KTP
∠ KLM =∠ KTP ....(Given)
∠ LKM = ∠ TKP ....(common)
Δ KLM and Δ KTP ......(AA corollary)
`therefore ("Ar" triangle "KLM")/("Ar" triangle "KTP") = ("KL"/"KT")^2 = (9/5)^2 = 81/25`
i.e., 81 : 25
[The ration of areas of two similar triangle is equal to the ratio of square of their corresponding sides.]
APPEARS IN
संबंधित प्रश्न
In the given figure, ∠CAB = 90° and AD⊥BC. Show that ΔBDA ~ ΔBAC. If AC = 75cm, AB = 1m and BC = 1.25m, find AD.
The actual area of an island is 1872km2 . On a map, this area is 117 cm2. if the length of the coastline is 44cm on the map, find the length of its actual coastline.
A model of an aeroplane is made to a scale of 1 : 400. Calculate : the length, in m, of the aeroplane, if length of its model is 16 cm.
Equilateral triangles are drawn on the sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.
In ΔABC, D and E are the mid-point on AB and AC such that DE || BC.
If AD : BD = 4 : 5 and EC = 2.5cm, find AE.
In the figure, DE || AC and DC || AP. Prove that `"BE"/"EC" = "BC"/"CP"`
Find the scale factor in each of the following and state the type of size transformation:
Image length = 6cm, Actual length = 4cm.
Find the scale factor in each of the following and state the type of size transformation:
Model area = 75cm2, Actual area = 3cm2
D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that b2 = `"p"^2 + "a"x + "a"^2/4`
In any triangle _______ sides are opposite to equal angles
