Question

The area of a right-angled triangle is 84 cm2 and one of its sides forming right angle is 12 cm.

Find the other side.​

Answer 1

Base = 14 cm , Height = 12 cm , Hypotenuse = 18.44 cm

Step-by-step explanation:

We Have :-

A Right Angled Triangle :-

One side = 12 cm

Area = 84 cm²

To Find :-

The Other Side

Formula Used :-

$area \: of \: triangle \: = \: \dfrac{1}{2} \times base \times height \\ \\ pythagoras \: theorem : - \\ {hypotense}^{2} = {base}^{2} + {height}^{2}$

Solution :-

$area \: of \: triangle \: = \dfrac{1}{2} \times base \times height \\ \\ 84 \: = \dfrac{1}{2} \times base \times 12 \\ \\ 84 = base \times 6 \\ \\ base \: = \dfrac{84}{6} \\ \\ base = 14 \: cm \\ \\ so \: base \: of \: the \: triangle = 14 \: cm \\ \\ applying \: pythagoras \: theorem \\ \\ {hypotenuse}^{2} = {base}^{2} + {height}^{2} \\ \\ {hypotenuse}^{2} = {(14)}^{2} + {(12)}^{2} \\ \\ {hypotenuse}^{2} = 196 + 144 \\ \\ {hypotenuse}^{2} = 340 \\ \\ hypotenuse = \sqrt{340} \\ \\ hypotenuse = 18.44 \: cm$

Base = 14 cm , Height = 12 cm , Hypotenuse = 18.44 cm

Answer 2

Answer:

Given :-

• Area of a right angled triangle = 84 cm²
• Base = 12 cm

To Find :-

Height

Solution :-

We know that

${ \large{ \boxed{ \frak{Area = \dfrac{1}{2} \times base \times height}}}}$

Let the height be h

$\sf \implies \: 84 = \dfrac{1}{2} \times 12 \times h$

$\sf \implies \: 84 = 6 \times h$

$\sf \implies \: \dfrac{84}{6} = h$

${ \textsf{ \textbf{ \pink{ \underline{Height \: is \: 14 \: cm}}}}}$