Advertisements
Advertisements
Question
Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.
Advertisements
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
If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle
In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2 : 1. Prove that
`(i) 9 AQ^2 = 9 AC^2 + 4 BC^2`
`(ii) 9 BP^2 = 9 BC^2 + 4 AC^2`
`(iii) 9 (AQ^2 + BP^2 ) = 13 AB^2`
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
In an equilateral triangle ABC, D is a point on side BC such that BD = `1/3BC` . Prove that 9 AD2 = 7 AB2
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
In equilateral Δ ABC, AD ⊥ BC and BC = x cm. Find, in terms of x, the length of AD.
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 length of diagonal of the square whose side is 8 cm.
Find the side of the square whose diagonal is `16sqrt(2)` cm.
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 12, 15
From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.
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.
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?
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.
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
