Question

One leg of a right triangle is half the other and the hypotenuse has the length of 3cm. How long is each leg?

Answer 1

Given:

One leg of a right triangle is half the other and the hypotenuse has the length of 3 cm.

To find:

How long is each leg?

Solution:

Let "x" represents the length of the long leg of the right-angled triangle.

So,

The length of the other leg = $\frac{1}{2} \times long \:leg = \frac{x}{2}$

The length of the hypotenuse = 3 cm

Pythagoras Theorem: $\boxed{\bold{Hypotenuse^2 = Perpendicular^2 + Base^2}}$

Using the Pythagoras theorem for the given right-angled triangle, we get

$3 = \sqrt{x^2 + (\frac{x}{2} )^2}$

$\implies 3 = \sqrt{x^2 + \frac{x^2}{4} }$

$\implies 3 = \sqrt{\frac{4x^2 + x^2}{4} }$

$\implies 3 = \sqrt{ \frac{5x^2}{4} }$

squaring on both sides

$\implies 9 = \frac{5x^2}{4}$

$\implies 5x^2 = 36$

$\implies x^2 = 7.2$

$\implies \bold{x = 2.68\:cm }$

∴ $\frac{x}{2} = \frac{2.68}{2} = \bold{1.34\:cm}$

Thus, the length of each leg are:

$\boxed{\bold{Long\:leg = \underline{2.68\:cm}}}\\\\\boxed{\bold{Other\:leg = \underline{1.34\:cm}}}$

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Also View:

the hypotenuse of a right-angled triangle is 3√5 cm if the smaller side is tripled and the larger side is doubled the new hypotenuse becomes 15 cm find the length of each side of the triangle?

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In a right triangle, the length of the hypotenuse and a side are respectively 5cm and 3cm. What is the length of the remaining side?

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