Advertisements
Advertisements
प्रश्न
In ΔABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.
विकल्प
12 cm
20 cm
6 cm
14 cm
उत्तर
20 cm
Explanation:
In ΔABC, PQ || BC
∴ `("AP")/("PB") = ("AQ")/("QC")` ...(By proportionality theorem)
`\implies 4/6 = 8/("QC")`
`\implies` QC = `(8 xx 6)/4` = 12 cm
Now, AC = AQ + QC
= 8 + 12
= 20 cm.
संबंधित प्रश्न
In the following figure, DE || OQ and DF || OR, show that EF || QR.
In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle?
In the figure, given below, the medians BD and CE of a triangle ABC meet at G. Prove that:
- ΔEGD ~ ΔCGB and
- BG = 2GD from (i) above.
In the given figure, ∠ABC = 90° and BD⊥AC. If AB = 5.7cm, BD = 3.8cm and CD = 5.4cm, find BC.
In an isosceles ΔABC, the base AB is produced both ways in P and Q such that
AP × BQ = AC2.
Prove that ΔACP~ΔBCQ.
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.
In Δ ABC, DE || BC; DC and EB intersects at F. if `"DE"/"BC" = 2/7` , find `("Ar" (triangle "FDE"))/("Ar" (triangle "FBC"))`
Δ ABC is similar to Δ PQR. If AB = 6cm, BC = 9cm, PQ = 9cm and PR = 10.5cm, find the lengths of AC and QR.
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 model of a ship is made with a scale factor of 1 : 500. Find
The deck area of the model, if the deck area of the ship is 1500000 m2
The scale of a map is 1 : 200000. A plot of land of area 20km2 is to be represented on the map. Find
The area on the map that represents the plot of land.
On a map drawn to a scale of 1 : 25000, a triangular plot of a land is marked as ABC with AB= 6cm, BC = 8cm and ∠ ABC = 90° . Calculate the actual length of AB in km and the actual area of the plot in km2 .
A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find : OA, if OA' = 6 cm.
In fig.DE || BC ,AD = 1 cm and BD = 2 cm. what is the ratio of the ar(ΔABC) to the ar (ΔADE)?
Choose the correct alternative:
If ΔABC ~ ΔPQR and 4A (ΔABC) = 25 A(ΔPQR), then AB : PQ = ?
If ΔPQR, AB is drawn parallel to QR. If PQ = 9cm, PR = 6cm and PB = 4.cm, find the length of AP.
ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate: Length of AB, if A'B' = 5.4cm
On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The area of the plot in sq km
If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆LOP ~ ∆RPN
If figure OPRQ is a square and ∠MLN = 90°. Prove that ∆QMO ~ ∆RPN
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`)
If ∆ABC is an isosceles triangle with ∠C = 90° and AC = 5 cm, then AB is
PR = 26 cm, QR = 24 cm, ∠PAQ = 90°, PA = 6 cm and QA = 8 cm. Find ∠PQR
D is the mid point of side BC and AE ⊥ BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that c2 = `"p"^2 - "a"x + "a"^2/4`
In the given figure YH || TE. Prove that ΔWHY ~ ΔWET and also find HE and TE
Two similar triangles will always have ________ angles
From the figure, prove that ∆SUN ~ ∆RAY
ΔABC ~ ΔPQR, A(ΔABC) = 80 sq.cm, A(ΔPQR) = 125 sq.cm, then complete `("A"(Δ"ABC"))/("A"(Δ"PQR")) = 80/125 = (["______"])/(["______"])`, hence `"AB"/"PQ" = (["______"])/(["______"])`
In ΔPQR, S and T are points on PQ and PR respectively. `(PS)/(SQ) = (PT)/(TR)` and ∠PST = ∠PRQ. Prove that PQR is an isosceles triangle.
