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प्रश्न
The difference between the sides at the right angles in a right-angled triangle is 7 cm. the area of the triangle is `60 cm^2` . Find its perimeter.
उत्तर
Area of the triangle 60cm^2
Let the sides of the triangle be a, b and c, where a is the height, b is the base and c is hypotenuse of the triangle.
`a-b=7cm`
`a=7+b` ....................(1)
Area of triangle `=1/2xxbxxh`
⇒`60=1/2xxbxx(7+b)`
⇒ `120=7b+b^2`
⇒`b^2+7b+b^2`
⇒`(b+15) (b-8)=0`
⇒`b=-15 or 8`
Side of a triangle cannot be negative.
Therefore, b = 8 cm.
Substituting the value of b = 8 cm, in equation (1):
`a=7+8=15 cm`
`Now, a=15 cm, b=8cm`
Now, in the given right triangle, we have to find third side.
`"(Hyp)"^2="(First side)"^2+"(Second side)"^2`
⇒` Hyp^2` =`8^2+15^2`
⇒`Hyp^2=64+225 `
⇒`Hyp^2=289`
⇒`Hyp=17 cm`
So, the third side is 17 cm.
Perimeter of a triangle = a + b + c.
Therefore, required perimeter of the triangle 15 + 8 + 1740 cm
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