Q18 of 99 Page 267

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.


Let the base, perpendicular and Hypotenuse of right-angled triangle be b, p and h respectively.


We know, Perimeter of right-angled triangle = b + p + h


Given, perimeter = 30 cm


⇒ b + p + h = 30


⇒ b + p + 13 = 30 [∵ h, hypotenuse = 13 cm]


⇒ b = 17 – p [1]


Also, we know By Pythagoras theorem in right-angled triangle


(Hypotenuse)2 = (Base)2 + (Perpendicular)2


⇒ h2 = p2 + b2


⇒ (13)2 = p2 + (17 – p)2


⇒ 169 = p2 + p2 + 289 – 34p


⇒ 2p2 – 34p + 120 = 0


⇒ p2 – 17p + 60 = 0


⇒ p2 – 12p - 5p + 60 = 0


⇒ (p – 12)(p - 5) = 0


⇒ p = 12 cm or p = 5 cm


Case I: p = 12 cm


⇒ b = 17 – 12 = 5 cm


and we know, area of triangle



Case II: p = 5 cm


⇒ b = 17 – 5 = 12 cm


and we know, area of triangle



Therefore, Area of triangle is 30 cm2.


More from this chapter

All 99 →
16

If the length of each side of an equilateral triangle is increased by 1 meter, then its area will be increased by √3 sq. meter. Let us write by calculating the length of side of equilateral triangle.

 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.

 19

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.

 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.