Advertisements
Advertisements
प्रश्न
In triangle ABC, given below, AB = 8 cm, BC = 6 cm and AC = 3 cm. Calculate the length of OC.
Advertisements
उत्तर
We have Pythagoras theorem which states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.
In Δ AOC,
AC2 = AO2 + CO2
(3)2 = AO2 + x2
9 = AO2 + x2
9 - x2 = AO2 ...(i)
In Δ AOB,
AB2 = AO2 + BO2
(8)2 = AO2 + (6 + x)2
64 = AO2 + (6 + x)2
64 - (6 + x)2 = AO2 ...(ii)
From equation (i) and (ii)
9 - x2 = 64 - (6 + x)2
9 - x2 = 64 - (36 + x2 + 12x) ...[(a + b)2 = a2 + 2ab + b2]
9 - x2 = 64 - 36 - x2 - 12x
9 = 28 - 12x
12x = 28 - 9
x = `19/12`
x = `1 7/12`
APPEARS IN
संबंधित प्रश्न
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD
ABC is an equilateral triangle of side 2a. Find each of its altitudes.
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2
In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.
PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
Which of the following can be the sides of a right triangle?
1.5 cm, 2 cm, 2.5 cm
In the case of right-angled triangles, identify the right angles.
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.
AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.
If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.
Find the Pythagorean triplet from among the following set of numbers.
4, 7, 8
The sides of the triangle are given below. Find out which one is the right-angled triangle?
8, 15, 17
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2AD2 + `(1)/(2)"BC"^2`
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)
In a square PQRS of side 5 cm, A, B, C and D are points on sides PQ, QR, RS and SP respectively such as PA = PD = RB = RC = 2 cm. Prove that ABCD is a rectangle. Also, find the area and perimeter of the rectangle.
If ‘l‘ and ‘m’ are the legs and ‘n’ is the hypotenuse of a right angled triangle then, l2 = ________
In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
(i) `"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
(ii) `"AB"^2 = "AD"^2 - "BC"."DM" + (("BC")/2)^2`
(iii) `"AC"^2 + "AB"^2 = 2"AD"^2 + 1/2"BC"^2`
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.
