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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

`Triangledef ~ Trianglemnk`. If De = 5 and Mn = 6, Then Find the Value of `(A(Triangledef))/(A(Trianglemnk))` - Geometry Mathematics 2

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प्रश्न

`triangleDEF ~ triangleMNK`. If DE = 5 and MN = 6, then find the value of `(A(triangleDEF))/(A(triangleMNK))`

उत्तर

`(A(triangleDEF))/(A(triangleMNK))` = `(DE)^2/(MN)^2 = 25/36` (Ratio of areas of similar triangles is equal to squares of corresponding sides)

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2017-2018 (March) Set A

संबंधित प्रश्‍न

In the given figure, two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that

(i) ΔPAC ∼ ΔPDB

(ii) PA.PB = PC.PD


In ΔABC and ΔDEF, it is being given that: AB = 5 cm, BC = 4 cm and CA = 4.2 cm; DE=10cm, EF = 8 cm and FD = 8.4 cm. If AL ⊥ BC and DM ⊥ EF, find AL: DM.


State, true or false:

Two similar polygons are necessarily congruent.


State, true or false:

Two congruent polygons are necessarily similar.


In the given figure, ∆ABC and ∆AMP are right angled at B and M respectively.

Given AC = 10 cm, AP = 15 cm and PM = 12 cm.

  1. Prove that: ∆ABC ~ ∆AMP
  2. Find: AB and BC.


In a right triangle ABC, right angled at B, D is a point on hypotenuse such that BD ⊥ AC , if DP ⊥ AB and DQ ⊥ BC then prove that
`(a)  DQ^2  Dp.QC (b)  DP ^2 DQ.AP 2 `  

 


The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, find the length of QR. 


In ΔABC, D and E are the midpoints of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC. 

 


In ΔPQR, PQ = 10 cm, QR = 12cm, PR = 8 cm, find the biggest and the smallest angle of the triangle.


If Δ ABC , MN || BC .

If AN : AC= 5 : 8, find ar(Δ AMN) : ar(Δ ABC) 


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"))`


ABCD and PQRS are similar figures. AB= 12cm, BC=x cm, CD= 15 cm, AD= 10 cm, PQ= 8 cm, QR = 5 cm, RS = m cm and PS = n cm .Find the values of x, m and n. 


The length of a river in a map is 54cm. if lcm on the map represents 12500m on land, find the length of the river. 


In fig.DE || BC ,AD = 1 cm and BD = 2 cm. what is the ratio of the ar(ΔABC) to the  ar (ΔADE)?


In ΔABC, DE is parallel to BC and DE = 3:8.

Find:
(i) AD : BD
(ii) AE, if AC = 16.


ΔABC is enlarged, with a scale factor 5. Find: BC, f B'C' = 16cm


The scale of a map is 1 : 50000. The area of a city is 40 sq km which is to be represented on the map. Find: The length of a scale in km represented by 1cm on the map.


In the given figure YH || TE. Prove that ΔWHY ~ ΔWET and also find HE and TE


In a square of side 10 cm, its diagonal = ______.


It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`. Then, `(ar(PRQ))/(ar(BCA))` is equal to ______.


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