Question

the perimeter of a triangle is 30cm it hypotenus is 13cm then? what are two sides?​

Answer 1

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Answer 2

Given,

Perimeter=30 cm

Hypotenus=13 cm

Answer,

12 and 5

Formula's,

• Perimeter of triangle
• Angle sum property

Solution,

Let the two sides of triangle be x ans z.

It's hypotenus is 13 cm[given]

Perimeter of triangle=Sum of all sides

=x+y+13

Perimeter=30 cm[given]

${hypotenus}^{2} = {perpendicular}^{2} + {base}^{2}$

${13}^{2} = {x}^{2} + {y}^{2}$

$169 = {x}^{2} + {y}^{2} | 2$

Substitute the value of x from 1into 2.

$169 = (17 - y {)}^{2} + {y}^{2}$

$169 = 289 + {y}^{2} - 34y + {y}^{2}$

$169 = 289 + {2y}^{2} - 34y$

${2y}^{2} - 34y + 120 = 0$

${y}^{2} - 12y- 5y + 60 = 0$

$y(y - 12) - 5(y - 12) = 0$

$(y - 5)(y - 12) = 0$

y =5,12

When y=5,

x=17-y=17-5=12.

When y=12,

x=17-y=17-12=5

Hence 12 and 5 are answers.