Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given:
∆ ABC
∠ADB = 90° and AC = AB = 26 cm
AD = 24 cm
To find : Length of BC In right angled ∆ ADC
AB = 26 cm, AD = 24 cm
According to Pythagoras Theorem,
(AC)2 = (AD)2 + (DC)2
(26)2 = (24)2 + (DC)2
676 = 576 + (DC)2
⇒ (DC)2 = 100
⇒ DC =`sqrt100` = 10 cm
∴ Length of BC = BD + DC
= 10 + 10 = 20 cm
APPEARS IN
RELATED QUESTIONS
Side of a triangle is given, determine it is a right triangle.
`(2a – 1) cm, 2\sqrt { 2a } cm, and (2a + 1) cm`
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
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`
Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]
km. Find their speed per hour.
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m;
find the distance between their tips.
In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm
Use the information given in the figure to find the length AD.
A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.
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
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
