Advertisements
Advertisements
Question
The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.
Solution
Let the corresponding sides of similar triangles be s1 and s2.
Let A1 and A2 be their corresponding areas.
s1 : s2 = 3 : 5 ......[Given]
∴ `s_1/s_2 = 3/5` ......(i)
`A_1/A_2 = (s_1^2)/(s_2^2)` .......[Theorem of areas of similar triangles]
= `((s_1)/(s_2))^2`
= `(3/5)^2` ......[From (i)]
= `9/25`
∴ Ratio of areas of similar triangles = 9 : 25
APPEARS IN
RELATED QUESTIONS
Prove that the area of the triangle BCE described on one side BC of a square ABCD as base is one half the area of the similar Triangle ACF described on the diagonal AC as base
D, E, F are the mid-point of the sides BC, CA and AB respectively of a ∆ABC. Determine the ratio of the areas of ∆DEF and ∆ABC.
D and E are points on the sides AB and AC respectively of a ∆ABC such that DE || BC and divides ∆ABC into two parts, equal in area. Find
D, E and F are respectively the mid-points of sides AB, BC and CA of ΔABC. Find the ratio of the area of ΔDEF and ΔABC.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals
Triangles ABC and DEF are similar If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ΔABC and ΔDEF.
The areas of two similar triangles are 169 cm2 and 121 cm2 respectively. If the longest side of the larger triangle is 26 cm, find the longest side of the smaller triangle.
In ABC, P divides the side AB such that AP : PB = 1 : 2. Q is a point in AC such that PQ || BC. Find the ratio of the areas of ΔAPQ and trapezium BPQC.
The areas of two similar triangles are 100 cm2 and 49 cm2 respectively. If the altitude the bigger triangle is 5 cm, find the corresponding altitude of the other.
The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5 cm, find the length of QR.
If ΔABC and ΔBDE are equilateral triangles, where D is the mid-point of BC, find the ratio of areas of ΔABC and ΔBDE.
If ∆ABC ~ ∆PQR and AB : PQ = 2 : 3, then fill in the blanks.
\[\frac{A\left( ∆ ABC \right)}{A\left( ∆ PQR \right)} = \frac{{AB}^2}{......} = \frac{2^2}{3^2} = \frac{......}{.......}\]
Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm, then Find corresponding side of the bigger triangle.
In the given figure 1.66, seg PQ || seg DE, A(∆PQF) = 20 units, PF = 2 DP, then Find A(◻DPQE) by completing the following activity.
The perpendicular from A on side BC of a Δ ABC meets BC at D such that DB = 3CD. Prove that 2AB2 = 2AC2 + BC2.
Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
O is a point on side PQ of a APQR such that PO = QO = RO, then ______.
If ΔABC ~ ΔPQR, AB : PQ = 4 : 5 and A(ΔPQR) = 125 cm2, then find A(ΔABC).
Find the length of ST, if ΔPQR ∼ ΔPST.
