Advertisements
Advertisements
Question
Triangles ABC and DEF are similar.
If area (ΔABC) = 36 cm2, area (ΔDEF) = 64 cm2 and DE = 6.2 cm, find AB.
Solution
Area (Δ ABC) = 36 cm2
Area (Δ DEF) = 64 cm2
DE = 6.2 cm
AB =?
We have
`"area (Δ ABC)"/"area (Δ DEF)" = "AB"^2/"DE"^2`
⇒ `(36)/(64) = "AB"^2/(6.2)^2`
⇒ AB = `(6)/(8)`
⇒ AB = `(6 xx 6.2)/(8)`
⇒ AB = 4.65 cm.
APPEARS IN
RELATED QUESTIONS
In the figure, given below, straight lines AB and CD intersect at P; and AC || BD. Prove that: If BD = 2.4 cm, AC = 3.6 cm, PD = 4.0 cm and PB = 3.2 cm; find the lengths of PA and PC.
P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: DL : DP = AL : DC.
In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO; show that: ΔAOB is similar to ΔCOD.
In the following figure, ABCD to a trapezium with AB || DC. If AB = 9 cm, DC = 18 cm, CF = 13.5 cm, AP = 6 cm and BE = 15 cm.
Calculate:
- EC
- AF
- PE
Triangle ABC is similar to triangle PQR. If AD and PM are corresponding medians of the two triangles, prove that : `("AB")/("PQ") = ("AD")/("PM")`.
In the following figure, ∠AXY = ∠AYX. If `(BX)/(AX) = (CY)/(AY)`, show that triangle ABC is isosceles.
In the figure given below, AB ‖ EF ‖ CD. If AB = 22.5 cm, EP = 7.5 cm, PC = 15 cm and DC = 27 cm. Calculate : AC
In the given figure, AB and DE are perpendiculars to BC.
Prove that : ΔABC ~ ΔDEC
In ΔABC, and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.
On a map drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = 90°.
Calculate:
- the actual lengths of AB and BC in km.
- the area of the plot in sq. km.
