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in Perimeter and Area of Plane Figures by (30.3k points)
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The difference between the sides at the right angles in a right-angled triangle is 7 cm. the area of the triangle is 60 cm2 . Find its perimeter.

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Given:

Area of the triangle = 60cm2

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 = 7 cm

a = 7 + b   ........(1)

Area of triangle = \(\frac{1}{2}\times b\times h\)

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.

So, the third side is 17 cm.

Perimeter of a triangle = a + b + c.

Therefore, required perimeter of the triangle 15 + 8 + 17 = 40 cm

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