Advertisements
Advertisements
Question
The ratio between the corresponding sides of two similar triangles is 2 is to 5. Find the ratio between the areas of these triangles.
Solution
We know that the ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
Required ratio = `2^2/5^2 = 4/25`
APPEARS IN
RELATED QUESTIONS
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"`
See the given figure. DE || BC. Find AD.
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles
In triangle ABC, AD is perpendicular to side BC and AD2 = BD × DC. Show that angle BAC = 90°.
The given diagram shows two isosceles triangles which are similar. In the given diagram, PQ and BC are not parallel; PC = 4, AQ = 3, QB = 12, BC = 15 and AP = PQ.
Calculate:
- the length of AP,
- the ratio of the areas of triangle APQ and triangle ABC.
In the figure, parts of the two triangles bearing identical marks are
congruent. State the test by which the triangles are congruent.
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")`.
In ΔABC, D and E are the points on sides AB and AC respectively. Find whether DE || BC, if:
- AB = 9 cm, AD = 4 cm, AE = 6 cm and EC = 7.5 cm.
- AB = 6.3 cm, EC = 11.0 cm, AD = 0.8 cm and AE = 1.6 cm.
Construct a triangle similar to a given triangle LMN with its sides equal to `4/5` of the corresponding sides of the triangle LMN (scale factor `4/5 < 1`)
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.