Question

The lengths of the sides of a right triangle are a and b, and the hypotenuse is

Answer 1

Answer:

Area is 2√3 ft².

Step-by-step explanation:

Given,

A right triangle having sides,

a = 2√3 ft,

c = 4 ft,

Where, c is the hypotenuse of the triangle,

If b is the other leg of the triangle,

By the pythagorean theorem,

$c^2=a^2+b^2$

$4^2=(2\sqrt{3})^2+b^2$

$16=12+b^2$

$4=b^2$

$\implies b = 2$

Hence, the area of the given triangle is,

$A=\frac{1}{2}\times a\times b$

$=\frac{1}{2}\times 2\sqrt{3}\times 2$

$=\frac{4\sqrt{3}}{2}$

$=2\sqrt{3}\text{ square ft}$

Answer 2

A^2+b^2=c^2
(2sqrt3)^2+b^2=16
12+b^2=16
solve for b
b=2
Now triangle area is A=1/2 bh
so
A=(1/2)(2)(2sqrt3)
A=2sqrt3