Question

Find x value.in this triangle. ​

Answer 1

Hi,

Explanation:

Since i have draw the answer, i post it.

The value 3 of h in your picture is false

I have imagined the sign in B means perpendicular.

(maybe i am wrong)

Answer 2

`x=3√(15)\;\textsf{cm} \approx 11.6\; \sf cm`

Explanation:

The diagram shows a triangle with two of its sides measuring 12 cm and 5 cm. An altitude is drawn from the vertex between these sides, perpendicular to the opposite side, forming two smaller right triangles. One of these right triangles has legs of x cm and 3 cm, with a hypotenuse measuring 12 cm.

To find the value of x, we can use Pythagoras Theorem.

`\boxed{\begin{array}{l}\underline{\sf Pythagoras \;Theorem} \\\\\Large\text{$a^2+b^2=c^2$}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ and $b$ are the legs of the right triangle.}\\\phantom{ww}\bullet\;\textsf{$c$ is the hypotenuse (longest side) of the right triangle.}\\\end{array}}`

From observation of the triangle:

• a = 3 cm
• b = x
• c = 12 cm

Substitute the values of a, b and c into the formula and solve for x:

`\begin{aligned}3^2+x^2&=12^2\\9+x^2&=144\\9+x^2-9&=144-9\\x^2&=135\\√(x^2)&=√(135)\\x&=√(135)\\x&=√(3^2 \cdot 15)\\x&=√(3^2)√(15)\\x&=3√(15)\end{aligned}`

Therefore, the exact value of x is 3√(15) cm, which is approximately 11.6 cm (rounded to the nearest tenth).