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
The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
If P and Q are the points on side CA and CB respectively of ΔABC, right angled at C, prove that (AQ2 + BP2) = (AB2 + PQ2)
Find the side of the square whose diagonal is `16sqrt(2)` cm.
A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.
In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.
In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that: 9BP2 = 9BC2 + 4AC2
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2
In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.
Find the length of the support cable required to support the tower with the floor
In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?
The perimeters of two similar triangles ABC and PQR are 60 cm and 36 cm respectively. If PQ = 9 cm, then AB equals ______.
For going to a city B from city A, there is a route via city C such that AC ⊥ CB, AC = 2x km and CB = 2(x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
In a quadrilateral ABCD, ∠A + ∠D = 90°. Prove that AC2 + BD2 = AD2 + BC2
[Hint: Produce AB and DC to meet at E.]
The longest side of a right angled triangle is called its ______.
If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.
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.
