Question

The legs of a right triangle are in the ratio 3:4 and its area is 1014sq cm.Find its hypotenuse.

ANSWER IS 102 sq cm,12cm BUT I DONT KNOW THE SOLUTION.

Answer 1

let there legs is 3x and 4x

area of triangle = b*h/2
1014 = 3x*4x/2
1014 = 6x^2
$169 = {x}^{2}$
$x = 13$
thus there legs will be
3*13 = 39 cm
4*13 = 52 cm

in right angle triangle
${p}^{2} + {b }^{2} = {h}^{2}$
thus
${39}^{2} + {52}^{2} = {h}^{2}$
$1521 + 2704 = {h}^{2}$
${h}^{2} = 4225 \\ \\ h = 65$
thus hypotaneous will be 65 cm

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