Advertisements
Advertisements
प्रश्न
The areas of two similar triangles are 169cm2 and 121cm2 respectively. If the longest side of the larger triangle is 26cm, find the longest side of the smaller triangle.
उत्तर
It is given that the triangles are similar.
Therefore, the ratio of the areas of these triangles will be equal to the ratio of squares of their corresponding sides.
Let the longest side of smaller triangle be X cm.
`(ar("Larger triangle"))/(ar("Smaller triangle"))=(("'Longest side of larger trainglle" )^2)/((L"ongest side of smaller trainglle")^2)`
⇒ `169/121=26^2/x^2`
⇒ `x= sqrt((26xx26xx121)/169)`
= 22
Hence, the longest side of the smaller triangle is 22 cm.
APPEARS IN
संबंधित प्रश्न
Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.
In figure, QA and PB are perpendicular to AB. If AO = 10 cm, BO = 6 cm and PB = 9 cm. Find AQ
In figure, considering triangles BEP and CPD, prove that BP × PD = EP × PC.
In figure, ABCD is a trapezium with AB || DC. If ∆AED is similar to ∆BEC, prove that AD = BC.
In ∆ABC, DE is parallel to base BC, with D on AB and E on AC. If `\frac{AD}{DB}=\frac{2}{3}` , find `\frac{BC}{DE}.`
In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
Given `triangle ABC ~ triangle PQR`, if `(AB)/(PQ) = 1/3`, then find `(ar triangle ABC)/(ar triangle PQR)`
In the adjoining figure, ABC is a right angled triangle with ∠BAC = 90°.
1) Prove ΔADB ~ ΔCDA.
2) If BD = 18 cm CD = 8 cm Find AD.
3) Find the ratio of the area of ΔADB is to an area of ΔCDA.
In the given figure ABC is a triangle with ∠EDB = ∠ACB. Prove that Δ ABC ~ Δ EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm. And area of Δ BED = 9 cm2. Calculate the
(1) length of AB
(2) area of Δ ABC
State, true or false:
Two isosceles-right triangles are similar.
In the given figure, ∠CAB = 90° and AD⊥BC. Show that ΔBDA ~ ΔBAC. If AC = 75cm, AB = 1m and BC = 1.25m, find AD.
ΔABC~ΔPQR and ar(ΔABC) = 4, ar(ΔPQR) . If BC = 12cm, find 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 the following figure, seg BE ⊥ seg AB and seg BA ⊥ seg AD. If BE = 6 and \[\text{AD} = 9 \text{ find} \frac{A\left( \Delta ABE \right)}{A\left( \Delta BAD \right)} \cdot\]
In ΔPQR, PQ = 10 cm, QR = 12cm, PR = 8 cm, find the biggest and the smallest angle of the triangle.
An aeroplane is 30m long and its model is l5 cm long. If the total outer surface area of the model is 150 cm2 , find the cost of painting the outer surface of the aeroplane at Rs. 120 per m2, if 5O m2 is left out for windows.
If ΔABC ~ ΔPQR and ∠A = 60°, then ∠P = ?
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 the adjoining figure. BC is parallel to DE, area of ΔABC = 25 sq cm, area of trapezium BCED = 24 sq cm, DE = 14 cm. Calculate the length of BC.
The areas of two similar triangles are 169cm2 and 121cm2 respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.
Find the scale factor in each of the following and state the type of size transformation:
Image length = 8cm, Actual length = 20cm.
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 plot of land of area 20km2 is represented on the map with a scale factor of 1:200000. Find: The number of KM represented by 2cm on the map.
On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The diagonal distance of the plot in km
In Quadrilateral ABCD, side AD || BC, diagonal AC and BD intersect in point P, then prove that `"AP"/"PD" = "PC"/"BP"`
In a square of side 10 cm, its diagonal = ______.
In the given figure, ∠ACB = ∠CDA, AC = 8cm, AD = 3cm, then BD is ______.
Is the following statement true? Why? “Two quadrilaterals are similar, if their corresponding angles are equal”.
ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA.
