Question

In: Math

Find the length of the longest altitude of the ∆abc whose sides are 35 cm, 54 cm, and 61 cm respectively.

Find the length of the longest altitude of the ∆abc whose sides are 35 cm, 54 cm, and 61 cm respectively.

Solutions

Expert Solution

Given

 ABC be a triangle in which sides AB = 35 cm, BC = 54 cm, CA = 61 cm

Find out

We have to determine the a;altitude of the triangle

Solution

AreaofΔABC=√s(s−a)(s−b)(s−c)

where s is the perimeter

s = (35+54+61)/2 = 75 cm.

=√75(75−35)(75−54)(75−61)
=√75×40×21×14
=√25×3×4×2×5×7×3×7×2
=5×2×2×3×7√5=420√5cm2

Also we know that

AreaofΔABC=12×AB×Altitude
⇒12×35×CD=420√5
⇒CD=420×2√535
Therefore,CD=24√5
Hence, the length of altitude is 24√5cm


The length of altitude is 24√5cm.

Related Solutions

The areas of two similar triangles ABC and DEF are 144cm2 and 81cm2, respectively. If the longest side of larger triangle ABC is 36 cm, then the longest side of the smaller triangle DEF is
The areas of two similar triangles ABC and DEF are 144cm2 and 81cm2, respectively. If the longest side of larger triangle ABC is 36 cm, then the longest side of the smaller triangle DEF is (1) 20 cm (2) 26 cm (3) 27 cm (4) 30 cm
4. Define the width of a rectangle as the longest length of its sides. Given a...
4. Define the width of a rectangle as the longest length of its sides. Given a closed rectangle A in Rn and a partition P of A, define the mesh of P as the maximum width of its subrectangles. Prove that a bounded function f : A → R is integrable on A if and only if, for every > 0, there is a δ > 0 such that U(f, P) − L(f, P) < for every partition P of...
Suppose that a triangle has sides of length a = 15 cm, b = 37 cm,...
Suppose that a triangle has sides of length a = 15 cm, b = 37 cm, and c = 29 cm, then α = _______, β = ______., and γ =______ . Carefully round your answers to the nearest tenth of a degree, do not include units in your typed answers.
A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm....
A rectangular block of copper has sides of length 12 cm, 26 cm, and 37 cm. If the block is connected to a 5.4 V source across two of its opposite faces, find the following. (a) What is the maximum current the block can carry? (b) What is the minimum current the block can carry?
A square loop of wire with sides of length 34 cm is in a uniform magnetic...
A square loop of wire with sides of length 34 cm is in a uniform magnetic field perpendicular to its area. Part A If the field's strength is initially 110 mT and it decays to zero in 0.011 s , what is the magnitude of the average emf induced in the loop? Part B What would be the average emf if the sides of the loop were only 17 cm ? Express your answer using two significant figures.
A pendulum with a length of 35 cm swings back and forth as shown in the...
A pendulum with a length of 35 cm swings back and forth as shown in the figure above, at each turn around point it stops and it starts accelerating until reaching maxium velocity at the botton (equilibrium position), at which point it starts slowing down. If the maximum angle is 48 degrees, what is its maximum velocity in m/s? (Use g = 10.0 m/s2 and assume there is no friction)
A 50-gram mass is hanging from a spring whose unstretched length is 10 cm and whose...
A 50-gram mass is hanging from a spring whose unstretched length is 10 cm and whose spring constant is 2.5 N/m. In the list below are described five situations. In some of the situations, the mass is at rest and remains at rest. In other situations, at the instant described, the mass is in the middle of an oscillation initiated by a person pulling the mass downward 5 cm from its equilibrium position and releasing it. Ignore both air resistance...
Consider a double convex lens with a focal length of 35 cm. If a marble is...
Consider a double convex lens with a focal length of 35 cm. If a marble is placed 85 cm from the lens, what is the image distance? Enter your answer in cm.
a) The focal length of a converging lens is 35 cm. An object is placed 100...
a) The focal length of a converging lens is 35 cm. An object is placed 100 cm in front of the lens. Describe the image. b) The focal length of a converging lens is 35 cm. An object is placed 30 cm in front of the lens. Describe the image. c) The focal length of a diverging lens is 35 cm. An object is placed 100 cm in front of the lens. Describe the image. d) The focal length of...
Find the length and width of a rectangle whose perimeter is 21 meters and whose area...
Find the length and width of a rectangle whose perimeter is 21 meters and whose area is 20 square meters. Assign variables to the unknown(s)... Form a system of equations... Solve the system and state your answer in the context of the problem, show all steps clearly, be sure to check your answers:
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT