Advertisements
Advertisements
प्रश्न
In a right angled triangle, if length of hypotenuse is 25 cm and height is 7 cm, then what is the length of its base?
Advertisements
उत्तर
Let ∆ABC be the given right angled triangle.
AC = 25 cm, AB = 7 cm
In ∆ABC, ∠B = 90° ...[Given]
∴ AC2 = AB2 + BC2 ...[Pythagoras theorem]
∴ 252 = 72 + BC2
∴ 625 = 49 + BC2
∴ BC2 = 625 – 49
∴ BC2 = 576
∴ BC = 24 cm ...[Taking square root of both sides]
∴ The length of the base of the given right angle triangle is 24 cm.
APPEARS IN
संबंधित प्रश्न
The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR
A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
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.
In the given figure, AB//CD, AB = 7 cm, BD = 25 cm and CD = 17 cm;
find the length of side BC.
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 12, 15
The sides of the triangle are given below. Find out which one is the right-angled triangle?
40, 20, 30
A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2
From the given figure, in ∆ABQ, if AQ = 8 cm, then AB = ?
In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is ______.
If S is a point on side PQ of a ΔPQR such that PS = QS = RS, then ______.
In ∆PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a – b) = (c + d)(c – d).
Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.
The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.
The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground. Find the length of the ladder.
