Advertisements
Advertisements
प्रश्न
The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.
Advertisements
उत्तर
Pythagoras theorem 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.
First, we consider the ΔBDC and applying Pythagoras theorem we get,
DB2 = DC2 + BC2
DB2 = 122 + 32
DB2 = 144 + 9
DB2 = 153
Now, we consider the ΔABD and applying Pythagoras theorem we get,
DA2 = DB2 + BA2
132 = 153 + BA2
BA2 = 169 - 153
BA = 4
The length of AB is 4 cm.
APPEARS IN
संबंधित प्रश्न
Side of a triangle is given, determine it is a right triangle.
`(2a – 1) cm, 2\sqrt { 2a } cm, and (2a + 1) cm`
In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.
A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
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.
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.
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2
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.
Choose the correct alternative:
In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P?
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm
Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm
In the figure below, find the value of 'x'.
Find the Pythagorean triplet from among the following set of numbers.
2, 6, 7
A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.
In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2
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 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.
Find the length of the support cable required to support the tower with the floor
