Advertisements
Advertisements
प्रश्न
In the given figure, ∠B = 90°, XY || BC, AB = 12 cm, AY = 8cm and AX : XB = 1 : 2 = AY : YC.
Find the lengths of AC and BC.
उत्तर
Given that AX : XB = 1 : 2 = AY : YC.
Let x be the common multiple for which this proportion gets satisfied.
So, AX = 1x and XB = 2x
AX + XB = 1x + 2x = 3x
⇒ AB = 3x .….(A - X - B)
⇒ 12 = 3x
⇒ x = 4
AX = 1x = 4 and XB = 2x = 2 × 4 = 8
Similarly,
AY = 1y and YC = 2y
AY = 8 …(given)
⇒ 8 = y
∴ YC = 2y = 2 × 8 = 16
∴ AC = AY + YC
AC = 8 + 16
AC = 24 cm
∆ABC is a right angled triangle. ...(Given)
∴ By Pythagoras Theorem, we get
⇒ AB2 + BC2 = AC2
⇒ BC2 = AC2 - AB2
⇒ BC2 = (24)2 - (12)2
⇒ BC2 = 576 - 144
⇒ BC2 = 432
⇒ BC = `sqrt(432)`
⇒ BC = `2 xx 2 xx 3sqrt3`
⇒ BC = `bb(12sqrt3 " cm")`
APPEARS IN
संबंधित प्रश्न
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right traingle ,right-angled at B. Find the values of p.
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
In ∆PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS = 13, find QR.
If the sides of the triangle are in the ratio 1: `sqrt2`: 1, show that is a right-angled triangle.
In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1: 3.
Prove that : 2AC2 = 2AB2 + BC2
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
Diagonals of rhombus ABCD intersect each other at point O.
Prove that: OA2 + OC2 = 2AD2 - `"BD"^2/2`
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 Pythagorean triplet from among the following set of numbers.
4, 7, 8
A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.
From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = OA2 + OB2 + OC2 - OD2 - OE2 - OF2
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
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.
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?
Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of `(20 "km")/"hr"` and the second train travels at `(30 "km")/"hr"`. After 2 hours, what is the distance between them?
From given figure, In ∆ABC, If AC = 12 cm. then AB =?
Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = `square`
∴ ∆ABC is 30° – 60° – 90° triangle
∴ In ∆ABC by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC
∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ `square` = 6 and BC = `6sqrt(3)`
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.
If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.
