Q. 6 A5.0( 1 Vote )

# Fill in the blanks so that the following statements are true:

and are the altitudes of ΔABC. If AB = 12, AC = 9.9, AD = 8.1 and BE = 7.2, perimeter of ΔABC = _____.

Answer :

We have

Given that: AD and BE are altitudes of ∆ABC. ⇒ ∠ADC = ∠

In ∆ADC and ∆BEC,

∠ADC = ∠BEC [∵, ∠ADC = ∠BEC = 90° as AD and BE ]

∠ACD = ∠BCE [∵, ∠ACD and ∠BCE are same angles of the same triangles, so they obviously are equal]

⇒ By AA-corollary, we can say that ∆ADC ∼ ∆BEC for the correspondence of ADC ↔ BEC.

By definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.

⇒

⇒

⇒

⇒ BC = 8.8

So, perimeter of ∆ABC is given by

Perimeter of ∆ABC = AB + BC + AC

⇒ Perimeter of ∆ABC = 12 + 8.8 + 9.9

⇒ Perimeter of ∆ABC = 30.7

**Thus, perimeter of ∆ABC = 30.7.**

Rate this question :

Fill in the blanks so that the following statements are true:

In ΔABC, and are altitudes. If AB = 12, BC = 15 and AM = 9.6, then CN = _____.

Gujarat Board MathematicsFill in the blanks so that the following statements are true:

and are the altitudes of ΔABC. If AB = 12, AC = 9.9, AD = 8.1 and BE = 7.2, perimeter of ΔABC = _____.

Gujarat Board MathematicsIn ΔXYZ and ΔPQR, XYZ ↔ PQR is similarity. XY = 12, YZ = 8, ZX = 16, PR = 8. So, PQ + QR = ………….

Gujarat Board MathematicsFill in the blanks so that the following statements are true:

The correspondence ABC ↔ PQR is a similarity in Δ ABC and ΔPQR. AB = 16, AC = 8, PQ = 24, BC = 12, then QR + PR = ____.

Gujarat Board MathematicsFill in the blanks so that the following statements are true:

The correspondence ABC ↔ ZXY is a similarity in ΔABC and ΔXYZ. If AB = 12, BC = 9, CA = 7.5 and ZX = 10, then YZ + XY = ____.

Gujarat Board MathematicsIn ΔABC, the correspondence ABC ↔ BAC is similarity …….. of the following is true.

Gujarat Board MathematicsIn Δ ABC, ||, P ∈ , Q ∈ . If 4AP = AB and AQ = 4, then AC =

Gujarat Board MathematicsIn Δ PQR, P—M—Q and P—N—R. If PQ = 18, PM = 12, PR = 9 and NR = …, then ||

Gujarat Board MathematicsIn ΔABC, A—P—B, A—Q—C and ||. If PQ = 5, AP = 4, AB = 12, then BC = …….

Gujarat Board Mathematics