Question

The sides (other than hypotenuse) of a right triangle are in the ratio 3:4 . A rectangle is described on its hypotenuse, the hypotenuse being the longer side of the rectangle . The breadth of the rectangle is 4/5 of its length . find the shortest side of the right triangle if the perimeter of the rectangle is 180 cm.​

Answer 1

Answer:

Let the perpendicular and base be 3x and 4x

Hypotenuse=length(longer side)

By Pythagoras theoram:-

$H^2=(3x)^2+(4x)^2$

$H^2=9 {x}^{2} +16 {x}^{2}$

$H^2=25 {x}^{2}$

$H= \sqrt{25 {x}^{2} }$

H=5x

$Breath= \frac{4}{5 } \: \: of \: \: 5x$

Breath=4x

Perimeter of rectangle=2(l+b)

180cm=2(4x+5x)

180cm=2(9x)

18x=180cm

x=180cm/18

x=10cm

Hence,

Shortest side of right angled triangle=3x

=2(10cm)

=30cm

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Answer 2

Answer:

i have solved the problem

you can see it in attachment

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