Question 74

The sides of a right-angled triangle forming right angle are in the ratio 5 : 12. If the area of the triangle is 270 cm$$^2$$, then the length of the hypotenuse is

Solution

length of base = 5x

length of height = 12x

area = $$\frac{1}{2} \times 5x \times 12x = 270 $$

$$ 30 \times x^2 = 270 $$

x = 3

base = $$ 5 \times 3 = 15 $$

height = $$ 12 \times 3 = 36 $$

We know that for a right angled triangle, $$ hypotenuse ^2 = side^2 + side^2 $$

$$ h^2 = b^2 + l^2 $$

= $$ 15^2 + 36^2 $$

= 225 + 1296

= 1521

$$ h = \sqrt 1521 = 39 $$

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