Q19 of 99 Page 267

The lengths of the sides containing the right angle are 12 cm and 5 cm. Let us write by calculating the length of perpendicular drawn from vertex of right angle on hypotenuse.

Given, Length of the height of the right- triangle = 12cm


Length of base = 5cm


According to the Pythagoras theorem



⇒ AC2 + CB 2 = AB2


⇒ 122 + 52 = AB2


⇒ 144 + 25 = AB2


⇒ AB = √ 169


⇒ AB = 13 cm


Now, Area of triangle ABC = ……. Eq 1


⇒ Area of right Triangle ABC =


⇒ Area of right-angle triangle = 30 cm2


Now according to given condition CD is perpendicular to AB


⇒ Area of triangle ABC = AB × h (from eq 1)


⇒


⇒


⇒ h = 4.62cm


More from this chapter

All 99 →
17

The area of an equilateral triangle and area of square are in the ration √3 : 2. If the length of diagonal of square is 60 cm. let us write by calculating perimeter of that triangle.

 18

Length of hypotenuse and perimeter of a right-angle triangle are 13 cm and 30 cm. Let us write by calculating the area of triangle.

 20

The largested square is cut-out from a right-angled triangular region with length of 3 cm, 4 cm and 5 cm respectively in such a way that the one vertex of square lies on hypotenuse of triangle. Let us write by calculating the length of side of square.

 21

If each side of an equilateral triangle is 4 cm, the measure of heights is