Advertisements
Advertisements
प्रश्न
In the given figure, DE║BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x.
उत्तर
In ΔADE and ΔABC
∠𝐴𝐷𝐸 = ∠𝐴𝐵𝐶 (𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠 𝑖𝑛 𝐷𝐸 ∥ 𝐵𝐶)
∠𝐴𝐸𝐷 = ∠𝐴𝐶𝐵 (𝐶𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑎𝑛𝑔𝑙𝑒𝑠 𝑖𝑛 𝐷𝐸 ∥ 𝐵𝐶
By AA similarity criterion, ΔADE ~ ΔABC
If two triangles are similar, then the ratio of their corresponding sides are proportional
∴ `(AD)/(AB)=(AE)/(AC)`
⇒`( AD)/(AD+DB)=(AE)/(AE+EC)`
⇒` x/(x+3x+4)=(x+3)/(x+3+3x+19)`
⇒ `x/(4x+4)=(x+3)/(x+3+3x+19)`
⇒ `x/(2x+2)=(x+3)/(2x+11)`
⇒ `2x^2+11x=2x^2+2x+6x+6`
⇒ 3x=6
⇒ x=2
Hence, the value of x is 2.
APPEARS IN
संबंधित प्रश्न
State which pair of triangles in the given figure are similar. Write the similarity criterion used by you for answering the question, and also write the pairs of similar triangles in the symbolic form:
In the following figure, if ΔABE ≅ ΔACD, show that ΔADE ∼ ΔABC.
A vertical pole of a length 6 m casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
In ΔABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:
(i) ΔOMA and ΔOLC
(ii) `"OA"/"OC"="OM"/"OL"`
The sides of certain triangles are given below. Determine which of them right triangles are.
1.4cm, 4.8cm, 5cm
In figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to ______.
If in triangles ABC and DEF, `(AB)/(DE) = (BC)/(FD)`, then they will be similar, when ______.
In the given figure, ΔPQR is a right-angled triangle with ∠PQR = 90°. QS is perpendicular to PR. Prove that pq = rx.
In the given figure, DE ∥ BC, AE = a units, EC = b units, DE = x units and BC = y units. Which of the following is true?
Which of the following is NOT a similarity criterion of traingles?
