Advertisements
Advertisements
Question
Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.
Solution
The two sides (excluding hypotenuse) of a right-angled triangle are given as 24cm and 7cm
(hypotenuse)2 = (24cm)2 + (7cm)2
(hypotenuse)2 = 576cm2 + 49cm2
(hypotenuse)2 = 625cm2
(hypotenuse)2 = (25cm)2
Thus, the length of the hypotenuse of the triangle is 25cm.
APPEARS IN
RELATED QUESTIONS
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
P and Q are the mid-points of the sides CA and CB respectively of a ∆ABC, right angled at C. Prove that:
`(i) 4AQ^2 = 4AC^2 + BC^2`
`(ii) 4BP^2 = 4BC^2 + AC^2`
`(iii) (4AQ^2 + BP^2 ) = 5AB^2`
ABC is a right triangle right-angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB, prove that
(i) cp = ab
`(ii) 1/p^2=1/a^2+1/b^2`
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, 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.
ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
In the given figure, ∆ABC is an equilateral triangle of side 3 units. Find the coordinates of the other two vertices ?
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
Walls of two buildings on either side of a street are parallel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street, its top touches the window of the other building at a height 4.2 m. Find the width of the street.
Some question and their alternative answer are given. Select the correct alternative.
If a, b, and c are sides of a triangle and a2 + b2 = c2, name the type of triangle.
In ΔABC, Find the sides of the triangle, if:
- AB = ( x - 3 ) cm, BC = ( x + 4 ) cm and AC = ( x + 6 ) cm
- AB = x cm, BC = ( 4x + 4 ) cm and AC = ( 4x + 5) cm
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
In the figure below, find the value of 'x'.
Find the Pythagorean triplet from among the following set of numbers.
9, 40, 41
Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.
PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.
Choose the correct alternative:
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
In ΔABC, if DE || BC, AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then value of x is ______.
If the areas of two circles are the same, they are congruent.
