Q. 115.0( 2 Votes )

# A boy is designing a diamond shaped kite, as shown in the figure where AE = 16 cm, EC = 81 cm. He wants to use a straight cross bar BD. How long should it be?

Answer :

To find DB

Let ∠EAD = x ----(1)

⇒ ∠ADE = 90 – x (∵ AED = 90 and sum of angles of triangle is 180)

⇒ ∠EDC = x (∵ ∠ADC = 90) ----(2)

⇒ ∠EAD = ∠EDC (by (1) and (2)) ----(3)

Now,

In ΔAED and ΔDEC

∠AED = ∠DEC (both perpendicular to AC)

∠EAD = ∠EDC (by (3))

∴ ΔAED ∼ ΔDEC

(∵ ΔAED ∼ ΔDEC)

⇒ 16×81 = ED^{2}

⇒ ED = 36 cm

⇒ 2×ED = DB = 72 cm

Rate this question :

From the given figure, identify the wrong statement.

Tamil Nadu Board - Math

The points D and E are on the sides AB and AC of ΔABC respectively, such that DE || BC. If AB = 3 AD and the area of Δ ABC is 72 cm^{2}, then find the area of the quadrilateral DBCE.

Find the unknown values in each of the following figures. All lengths are given in centimeters. (All measures are not in scale)

Tamil Nadu Board - Math

A boy is designing a diamond shaped kite, as shown in the figure where AE = 16 cm, EC = 81 cm. He wants to use a straight cross bar BD. How long should it be?

Tamil Nadu Board - Math

The perimeters of two similar triangles are 24 cm and 18 cm respectively. If one side of the first triangle is 8 cm, then the corresponding side of the other triangle is

Tamil Nadu Board - MathFind the unknown values in each of the following figures. All lengths are given in centimeters. (All measures are not in scale)

Tamil Nadu Board - Math

In ΔABC, AB = AC and BC = 6 cm. D is a point on the side AC such that AD = 5 cm and CD = 4 cm. Show that ΔBCD ~ ΔACB and hence find BD.

Tamil Nadu Board - Math