Question

Please help with the question in the attachment, mind that AC = x+2 it is equal to x+3 as shown in the triangle. Whoever get the answer correct I'll mark them brainliest. Thanks in advance.

Answer 1

From the theorem of Pythagoras,

In ΔABC,

AC²=AB²+BC²

(x+3)² = x² + 9²

x²+6x+9 = x²+81

6x = 72

x = 12

Answer 2

The given Figure is a right angled triangle and we are asked to find the value of x.

By using the Pythagoras theorem we can find the required value.

Let's get started :D

$\bigstar \large \purple{ \pmb{ \sf Solution}}$

$\underline{ \boxed {\pink{{ \frak{ {h(hypotenuse)}^{2} = {p(perpendicular)}^{2} + {b(base)}^{2} }}}}} \bigstar$

• The above is what Pythagoras theorem states... that... the square of hypotenuse of a right angles triangle is equal to the sum of the squares of its perpendicular and base
• Hypotenuse is the longest side and it is opposite side of the 90⁰

We are provided with the following values :-

• AB = $\sf x$
• BC = $\sf 9$
• CA = $\sf x+3$

Now, according to the figure, CA is the side opposite to 90⁰ . Hence, it is the hypotenuse.

$\: \: \: \: \: \: \: \: \: \dag\underline \frak{substituting \: the \: values \: in \: formula : - }$

$: \implies \sf {(x + 3)}^{2} = {9}^{2} + {x}^{2}$

we know that:-

• $\large\underline{ \boxed{ \pink{{ \frak{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}}}}} \bigstar$

$: \implies\large \sf \cancel{{x}^{2} } + 9 + 6x = 81 + \cancel{ {x}^{2} }$

$: \implies \large\sf 6x = 72$

$: \implies \large{\boxed {\pink{{ \frak{x = 12}}}}} \bigstar$

And we are done :D