Question

The hypothesis of a right triangle is 13 cm and one side is 12 cm find the area.

Answer 1

Answer:

Hypotenuse of a right angle triangle (H) = 13cm

One side (B) = 12cm

We know that,

By pythagoras theorm,

${h}^{2} = {b}^{2} + {p}^{2} \\ {13}^{2} = {12}^{2} + {p}^{2} \\ 169 - 144 = {p}^{2} \\ {p}^{2} = 25 \\ p = \sqrt{25} \\ p = 5cm$

Area =

$\frac{1}{2} \times b \times p \\ \frac{1}{2} \times 12 \times 5 \\ = 30cm$

Answer 2

Answer:

$\setlength{\unitlength}{1.2 cm}\begin{picture}(0,0)\linethickness{0.7mm}\qbezier(1, 0)(1,0)( 1,3)\qbezier(5,0)(5, 0)(1,3)\qbezier(5,0)(1,0)(1,0)\put(1,0){\dashbox{1}(1,0.5)}\put(0.6,3){ \sf A }\put(3.3,1.5){13 cm}\put(0.6,-0.2){ \sf B }\put(2.5,-0.3){12 cm}\put(5.1, - 0.2){ \sf C }\end{picture}$

Let ∆ ABC be the right angle triangle, right angled at B.

• By Phythagoras theorem we get :

➝ AC² = AB² + BC²

➝ (13)² = AB² + (12)²

➝ 169 = AB² + 144

➝ AB² = 169 - 144

➝ AB² = 25

➝ AB = 5 cm

❒ According to Question now,

➸ Area of ∆ABC = ½ × Base × Height

➸ Area of ∆ABC = ½ × 5 × 12

➸ Area of ∆ABC = 5 × 6

➸ Area of ∆ABC = 30 cm²