Advertisements
Advertisements
प्रश्न
In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.
Advertisements
उत्तर
In ΔABC, ∠B = 90°
∴ AC2 = AB2 + BC2 ....(Pythagoras Theorem)
⇒ 102 = AB2 + 62
⇒ AB2 = 102 - 62
= 100 - 36
= 64
Now,
BD = BC + CD
= 6 + 9
= 15cm
⇒ BD2 = 225
In ΔABD, ∠B = 90°
∴ AD2 = AB2 + BD2
⇒ AD2 = 64 + 225 = 289
⇒ AD = 17cm.
APPEARS IN
संबंधित प्रश्न
In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.
In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
`"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
In equilateral Δ ABC, AD ⊥ BC and BC = x cm. Find, in terms of x, the length of AD.
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
Prove that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
The sides of a certain triangle is given below. Find, which of them is right-triangle
16 cm, 20 cm, and 12 cm
In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________
Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Give reason
In the figure, find AR
From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?
In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is ______.
A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.
Points A and B are on the opposite edges of a pond as shown in the following figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
