The sides of a right triangle are 6, 8, and 10. Find the altitude draw

Question

The sides of a right triangle are 6, 8, and 10. Find the altitude drawn to the hypotenuse.

(A) 2.4
(B) 3.4
(C) 3.5
(D) 4.2
(E) 4.8

Abhishek009 · Answer

\frac{6*8}{2} = \frac{10*a}{2}

So,  a = 4.8  , Answer must be (E)

abhinavsodha800 · Answer

Hi Abhishek,
How you got 10 * a /2 ?

oldmonkey · Answer

Area of a triangle is 1/2 (b*h)

In this case 1/2 * (product of the lengths of the legs of the hypotenuse triangle) = 1/2 * ( length of altitude from the vertex opp the hypo *the lentgh of the hypo.)
let x be the length of the altitude

hence 1/2 (8*6) = 1/2 (x*10)

solving x = 4.8

abhinavsodha800 · Answer

Hi Old monkey how did you arrived with the formulae of 1/2 b * h = 1/2 ( lenght of altitude * length of hypotenuse)

oldmonkey · Answer

Formula for area of the triangle which is 1/2 * (base) * (height)

The legs are the perpendicular sides of the triangle

The altitude is perpendicular to the hypotenuse

Refer figure its should get clear

CEdward · Answer

The altitude bissects the 90 degree angle of triangle ABC so the result is 2 45-45-90 triangles.

8 is the hypotenuse for one of those triangles with side lengths in the ratio x:x:x√2

8 = x√2 ---> x = 4√2 = 4 x 1.4 = 4.8

E.

The sides of a right triangle are 6, 8, and 10. Find the altitude draw

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The sides of a right triangle are 6, 8, and 10. Find the altitude draw

Prep Toolkit

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