the base of a right triangle is 1 cm more than the twice of its height and its area is 18 square cm find the base and height of a triangle

Open in App

Solution

Dear Student,

$L e t t h e h e i g h t o f t h e t r i a n g l e b e h c m a n d t h e b a s e o f t h e t r i a n g l e b e b c m . A c c o r d i n g t o t h e q u e s t i o n : b = 2 h + 1 A r e a o f t r i a n g l e = \frac{1}{2} \times B a s e \times H e i g h t = \frac{1}{2} \times b \times h 18 = \frac{1}{2} \times (2 h + 1) \times h 18 \times 2 = 2 h^{2} + h 36 = 2 h^{2} + h 2 h^{2} + h - 36 = 0 2 h^{2} + 9 h - 8 h - 36 = 0 h (2 h + 9) - 4 (2 h + 9) = 0 (h - 4) (2 h + 9) = 0 S o, h - 4 = 0 o r 2 h + 9 = 0 \Rightarrow h = 4 c m o r h = \frac{- 9}{2} c m S i n c e, h i s a l e n g t h m e a s u r e, i t c a n n o t b e n e g a t i v e . H e n c e, h = 4 c m b = 2 h + 1 = 2 (4) + 1 = 8 + 1 = 9 c m S o, H e i g h t o f t r i a n g l e i s 4 c m a n d B a s e o f t r i a n g l e i s 9 c m .$

Regards

Suggest Corrections

Similar questions

6

108

^{2}

The base and height of the triangle are in the ratio 3:2. If the area of the triangle is 243 cm $^{2}$ , find the base and height of the triangle.

Join BYJU'S Learning Program