Advertisements
Advertisements
Question
ΔABC ∼ ΔDEF and A(ΔABC) : A Δ(DEF) = 1 : 2 If AB = 4 find DE.
Solution
(1) Δ ABC ∼ Δ DEF
`(A(DeltaABC))/(A(DeltaDEF)) = (AB)^2/(DE)^2`
`1/2 = 4^2/(DE^2)`
`1/2 = 16/(DE^2)`
∴ `DE^2 = 16 × 2 ∴ DE = 4sqrt2`
APPEARS IN
RELATED QUESTIONS
In the figure given below, Ray PT is bisector of ∠QPR. If PQ = 5.6 cm, QT = 4 cm and TR = 5 cm, find the value of x .
In the following figure, if LM || CB and LN || CD, prove that `("AM")/("AB")=("AN")/("AD")`
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that `("AO")/("BO") = ("CO")/("DO")`
In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form:
In the given figure, DB⊥BC, DE⊥AB and AC⊥BC.
Prove that `(BE)/(DE)=(AC)/(BC)`
State the SAS-similarity criterion
In ∆ABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB. If seg AB ≅ seg AC then prove that ED || BC.
In ∆ABC, AP ⊥ BC, BQ ⊥ AC B– P–C, A–Q – C then prove that, ∆CPA ~ ∆CQB. If AP = 7, BQ = 8, BC = 12 then Find AC.
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.
In Δ ABC, D and E are points on the sides AB and AC respectively. If AD= 4cm, DB=4.Scm, AE=6.4cm and EC=7.2cm, find if DE is parallel to BC or not.
A triangle LMN has been reduced by scale factor 0.8 to the triangle L' M' N'. Calculate: the length of LM, if L' M' = 5.4 cm.
In the following figure, in Δ PQR, seg RS is the bisector of ∠PRQ.
PS = 11, SQ = 12, PR = 22. Find QR.
The sides PQ and PR of the ΔPQR are produced to S and T respectively. ST is drawn parallel to QR and PQ: PS = 3:4. If PT = 9.6 cm, find PR. If 'p' be the length of the perpendicular from P to QR, find the length of the perpendicular from P to ST in terms of 'p'.
In ΔABC, DE || BC such that AD =1.5 cm, DB = 3 cm and AE = 1 cm. Find AC.
ΔABC is enlarged, with a scale factor 5. Find: BC, f B'C' = 16cm
Two triangles QPR and QSR, right angled at P and S respectively are drawn on the same base QR and on the same side of QR. If PR and SQ intersect at T, prove that PT × TR = ST × TQ
In the adjacent figure, ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ~ ∆ADE and hence find the lengths of AE and DE
In the given figure the value of x is
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.
