Question

Base of right angled triangle is 5 cm and hypotenuse is 13 find area

Answer 1

Base is 5cm
Hypotenuse is 13cm
Let the height be x

Applying Pythagoras Theorm
(13)²=5²+x²
x² = (13)² - 5²
x = 12cm

Area of triangle = 1/2 × base × height
1/2×5×12
30cm²

Area is 30cm²

Answer 2

The area of the given triangle is $30\:cm^{2}$.

Tips:

The Pythagorean theorem states that if a be the vertical, b be the base and h be the hypotenuse of a right-angled triangle, then

$\boxed{a^{2}+b^{2}=c^{2}}$

Also, area is given by $\boxed{A=\dfrac{1}{2}ab}$

Step-by-step explanation:

Given, base = 5 cm and hypotenuse = 13 cm

Using Pythagorean theorem, we get

$(vertical)^{2}+(5)^{2}=(13)^{2}$

$\Rightarrow (vertical)^{2}+25=169$

$\Rightarrow (vertical)^{2}=169-25$

$\Rightarrow (vertical)^{2}=144$

$\Rightarrow vertical=\sqrt{144}$

• We take the positive value only, since length is positive.

$\Rightarrow vertical=12$

So, vertical is 12 cm.

Thus the area of the given triangle is

$\Delta=\dfrac{1}{2}\times base\times vertical$

$=\dfrac{1}{2}\times 5\times 12\quad cm^{2}$

$=30\quad cm^{2}$

#SPJ3