Question 126

The area of a right angled triangle is 80 sq. cm. The ratio of the base and the height of the triangle is 4 : 5. Find the length of hypotenuse.

Solution

Let base and height be $$4x$$ and $$5x$$ respectively.

Area of triangle = $$\frac{1}{2} \times$$ base $$\times$$ height = 80

=> $$\frac{1}{2} \times 4x \times 5x = 80$$

=> $$x^2 = \frac{80}{10} = 8$$

=> $$x = \sqrt{8} = 2 \sqrt{2}$$

=> Base = $$8 \sqrt{2}$$ and Height = $$10 \sqrt{2}$$

$$\therefore$$ Hypotenuse = $$\sqrt{(8 \sqrt{2})^2 + (10 \sqrt{2})^2}$$

= $$\sqrt{128 + 200} = \sqrt{328}$$

$$\approx 18$$ cm

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