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in Perimeter and Area of Plane Figures by (29.9k points)
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The perimeter of a right triangle is 40 cm and its hypotenuse measure 17 cm. Find the area of the triangle.

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The perimeter of a right-angled triangle = 40 cm

Therefore, a + b + c cm

Hypotenuse = 17 cm

Therefore, c = 17cm

a + b + c = 40 cm

\(\Rightarrow\) a + b + 17 = 40

\(\Rightarrow\) a + b = 23

\(\Rightarrow\) b = 23 - a    ......(i)

Now, using Pythagoras theorem, we have:

Substituting the value of a = 15, in equation (i) we get:

b = 23 - a

= 23 - 15

= 8 cm

If we had chosen a = 8 cm, then, b = 23 - 8 = 15 cm

In any case,

Area of triangle = \(\frac{1}{2}\)x base x height

\(\frac{1}{2}\times8\times15\)

= 60 cm2

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