Advertisements
Advertisements
Question
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
Solution
Hypotenuse = 65cm
One side = 16cm
Let the other side be of length x cm
By Pythagoras theorem,
(65cm)2 = (16cm)2 + (x cm)2
(x cm)2 = 4225cm2 - 256cm2
= 3969cm2
= (63cm)2
⇒ x = 63cm
Area of the triangle
= `(1)/(2) xx ("Base" xx "Height")`
= `(1)/(2) xx 16"cm" xx 63"cm"`
= 504cm2.
APPEARS IN
RELATED QUESTIONS
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right traingle ,right-angled at B. Find the values of p.
ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
Identify, with reason, if the following is a Pythagorean triplet.
(5, 12, 13)
Find the side and perimeter of a square whose diagonal is 10 cm.
In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF
In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.
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.
In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1: 3.
Prove that : 2AC2 = 2AB2 + BC2
In the following Figure ∠ACB= 90° and CD ⊥ AB, prove that CD2 = BD × AD
In ∆ ABC, AD ⊥ BC.
Prove that AC2 = AB2 +BC2 − 2BC x BD
Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.
Triangle PQR is right-angled at vertex R. Calculate the length of PR, if: PQ = 34 cm and QR = 33.6 cm.
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
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?
Sides AB and BE of a right triangle, right-angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is ______.
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.
