Question

in a right angled triangle, the area is 12cmsq. it is found that tan A is 2/3. find the length of the hypotenuse AC in cm.

Answer 1

in right angle triangle ABC , area=1/2AB*BC=12

given, tanA=2/3,it means,BC/AB=2/3

putting BC =2/3AB in as

1/2AB*2/3AB=12

(AB)²=36

AB=6

putting the value of AB in any eq. we get BC =4

then applying Pythagoras law, we get AC =√52

Answer 2

The correct answer is $2\sqrt{13}$.

Given: Area of triangle = 12 $cm^{2}$.

The value of tanA = $\frac{2}{3}$.

To Find: The length of hypotenuse.

Solution:

Area of triangle = $\frac{1}{2} *b*h$ = 12 $cm^{2}$.

$tanA=\frac{h}{b}=\frac{2}{3}$

3h = 2b

$h=\frac{2b}{3}$

Now, put the value of h in area of triangle equation.

12 = $\frac{1}{2}*b*\frac{2b}{3}$

72 = $2b^{2}$

$b^{2} =36$

b = 6

Put the value of b in $h=\frac{2b}{3}$.

h = $\frac{2*6}{3}$

h = 4

$(Hypotenuse)^{2}$ = $h^{2} +b^{2}$.

$(Hypotenuse)^{2} = 4^{2} +6^{2}$

$(Hypotenuse)^{2} = 16+36$

$(Hypotenuse)^{2} = 52$

$Hypotenuse = \sqrt{52}$ = $2\sqrt{13}$

Hence, the length of hypotenuse is $2\sqrt{13}$.

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